Rahasia Ilmu Eksakta

Matematika Keuangan: Diskon Tunai

<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2cxzso3vkDOto28X5_kCAXdegUpdWLHiBbG958M-IvmeMPhoBDEmaIquCYp9AjVOZ5y7qHgm0Z71jzUkiz8YOqxNAv36eCpQeeD0-O8vZGglbXODJa24M_SFZASxC3BCOEVEXT5K__Mc/s1600/diskon+tunai+2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-size: large;"><img border="0" height="215" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2cxzso3vkDOto28X5_kCAXdegUpdWLHiBbG958M-IvmeMPhoBDEmaIquCYp9AjVOZ5y7qHgm0Z71jzUkiz8YOqxNAv36eCpQeeD0-O8vZGglbXODJa24M_SFZASxC3BCOEVEXT5K__Mc/s320/diskon+tunai+2.jpg" width="320" /></span></a></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: justify; unicode-bidi: embed; word-break: normal;"><span style="font-size: large;">Para penjual di bidang marketing atau pemasaran melakukan berbagai cara agar produknya diminati banyak pembeli dan lebih meningkatkan omzet. Salah satu cara yang digunakan adalah, yaitu menyelenggarakan acara diskon. Acara diskon yang diselenggarakan penjual dapat diwujudkan dalam berbagai macam tema. </span><br /><a name='more'></a><span style="font-size: large;">Tema yang diselenggarakan berubah-ubah mengikuti situasi yang sedang terjadi. Untuk mendorong pembayaran yang lebih cepat,  banyak produsen dan pedagan grosir menawarkan potongan tunai untuk pembayaran jauh sebelum jatuh tempo. Besarnya potongan dan syaratnya biasanya dinyatakan dalam termin (credit term), seperti :  4/30    ;     n/100    yang artinya potongan tunai atau diskon tunai (cash discount) sebesar 2% akan diberikan jika pembayaran dilakukan dalam waktu 10 hari. Jika tidak, jumlah keseluruhan harus dilunasi dalam waktu 30 hari. Pembeli yang akan memanfaatkan potongan tunai, pada praktiknya akan menerima potongan atau bunga dimuka dalam bentuk diskon tunai. Tingkat bunga efektif yang didapatkan dengan cara ini biasanya sangat tinggi.</span></div><div style="text-align: justify;"><span style="font-size: large;"><br /></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: justify; unicode-bidi: embed; word-break: normal;"><span style="font-size: large;"><span style="font-family: 'Century Schoolbook';">Contoh</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">Soal</span><span style="font-family: 'Century Schoolbook';">:</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: justify; text-justify: inter-ideograph; unicode-bidi: embed; word-break: normal;"><span style="font-size: large;"><span style="font-family: 'Century Schoolbook';">Mbok</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">Srintil</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">membeli</span><span style="font-family: 'Century Schoolbook';">furniture </span><span style="font-family: 'Century Schoolbook';">seharga</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">Rp</span><span style="font-family: 'Century Schoolbook';">. 100.000.000,- </span><span style="font-family: 'Century Schoolbook';">dengan</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">termin</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">kredit</span><span style="font-family: 'Century Schoolbook';">  4/30  ,  n/100 </span><span style="font-family: 'Century Schoolbook';">Berapakah</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">bunga</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">efektif</span><span style="font-family: 'Century Schoolbook';"> yang </span><span style="font-family: 'Century Schoolbook';">ditawarkan</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">kepada</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">Mbok</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">Srintil</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">tadi</span><span style="font-family: 'Century Schoolbook';"> ?</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: justify; text-justify: inter-ideograph; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';"><span style="font-size: large;">      </span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: justify; text-justify: inter-ideograph; unicode-bidi: embed; word-break: normal;"><span style="font-size: large;"><span style="font-family: 'Century Schoolbook';">( </span><span style="font-family: 'Century Schoolbook'; font-weight: bold;">catatan</span><span style="font-family: 'Century Schoolbook';">: </span><span style="font-family: 'Century Schoolbook';">jika</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">Mbok</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">Srintil</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">tadi</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">ingin</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">mendapatkan</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">potongan</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">maka</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">ia</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">akan</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">membayarnya</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">pada</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">hari</span><span style="font-family: 'Century Schoolbook';"> ke-30 </span><span style="font-family: 'Century Schoolbook';">dan</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">jika</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">tidak</span><span style="font-family: 'Century Schoolbook';">, </span><span style="font-family: 'Century Schoolbook';">ia</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">harus</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">membayar</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">pada</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">hari</span><span style="font-family: 'Century Schoolbook';"> ke-100 </span><span style="font-family: 'Century Schoolbook';">atau</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">ada</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">waktu</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">perbedaan</span><span style="font-family: 'Century Schoolbook';"> 70 </span><span style="font-family: 'Century Schoolbook';">hari</span><span style="font-family: 'Century Schoolbook';">)</span></span></div><span style="font-family: 'Century Schoolbook';"></span><br /><div style="text-align: justify;"><span style="font-family: 'Century Schoolbook';"><span style="font-size: large;">Jawab:</span></span></div><span style="font-family: 'Century Schoolbook';"></span><br /><div><div class="O0" style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: large;"><span style="font-family: Wingdings; mso-special-format: bullet;">Ø</span>   Perbedaan jumlah yang di bayarkan atau diskon adalah 4% atau sebesar   Rp.100.000.000 X 4%  = Rp. 4.000.000,- <br /><br />  P = Rp.100.000.000 - Rp. 4.000.000 = Rp.  96.000.000 <br /><br /> SI = Rp. 4.000.000 <br /><br />  t  =  70/365 = 0,191 <br /><br />r =SI/Pt = (4.000.000/96.000.000(70/365)) = 4.000.000/18.366.000<br /><br />r = 0,2172 atau 21,72%<br /><br /><b>Cara 2:</b><br /><br />r = 365/70 x 0,04/0,96<br /><br />r = 5,214 X 0,0416<br />  = 0,2172 = 21, 72%</span></div></div><div class="O0" style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><br /></div><div class="O0" style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><br /></div></div>

Para penjual di bidang marketing atau pemasaran melakukan berbagai cara agar produknya diminati banyak pembeli dan lebih meningkatkan omzet. Salah satu cara yang digunakan adalah, yaitu menyelenggarak...

23Dec2015

Matematika Keuangan: WESEL

December 23, 2015 kantor pos , keuangan , Matematika , Materi , wesel

<div dir="ltr" style="text-align: left;" trbidi="on"><div class="MsoNormal" style="line-height: 150%;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMJdN7zgl4Skbb-NN2DEE46Q8j9a9_ZWBiSFeyiBmBp68dLzYN0xGGORgSRBSyg8fGtLMqJPNJS7backj9oWzYRDuOhJ0ymM7YBINKqVu7PHx3IvGQ-UkwgZO6Yb6K-JmZBwU9YucnhqI/s1600/wesel+%2528allmipa%2529.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="wesel" border="0" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMJdN7zgl4Skbb-NN2DEE46Q8j9a9_ZWBiSFeyiBmBp68dLzYN0xGGORgSRBSyg8fGtLMqJPNJS7backj9oWzYRDuOhJ0ymM7YBINKqVu7PHx3IvGQ-UkwgZO6Yb6K-JmZBwU9YucnhqI/s400/wesel+%2528allmipa%2529.jpg" title="wesel (allmipa)" width="400" /></a></div><br /><div class="MsoNormal" style="line-height: 150%;"><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;">Perhatikan gambar diamping. Ya benar, Gambar kuning yang terpapar tersebut bukan sesuatu yang asing bagi kalian, itulah yang namanya wesel. Wesel merupakan salah satu layanan PT. Pos Indonesia, yang memudahkan kita untuk melakukan pengiriman dan penerimaan uang. Mari kita pelajari lebih lanjut tentang materi pembahasan wesel di bawah ini, materi wesel ini dibahas dalam mata kuliah matematika keuangan, Simak ya kawan:</span><br /><a name='more'></a></div><div class="MsoNormal" style="line-height: 150%;"><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;"><br /></span></div><div class="MsoNormal" style="line-height: 150%;"><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;">Wesel atau <i>promissory notes</i> adalah janji tertulis seorang debitor (pembuat wesel) untuk membayar sejumlah uang kepada atau atas perintah dari kreditor (penerima wesel), dengan atau tanpa bunga, pada tanggal tertentu.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 150%;"><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;"><br /></span></div><div class="MsoListParagraphCxSpFirst" style="line-height: 150%; mso-list: l1 level1 lfo1; text-indent: -18.0pt;"><span lang="IN" style="font-family: Symbol; font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal; line-height: normal;">         </span></span><i><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;">interest bearing notes</span></i><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;"></span><span lang="IN" style="font-family: Wingdings; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-char-type: symbol; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-symbol-font-family: Wingdings;">à</span><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;">wesel yang mengandung bunga<o:p></o:p></span></div><div class="MsoListParagraphCxSpLast" style="line-height: 150%; mso-list: l1 level1 lfo1; text-indent: -18.0pt;"><span lang="IN" style="font-family: Symbol; font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; font-stretch: normal; line-height: normal;">         </span></span><i><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;">non-interest bearing notes</span></i><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;"> </span><span lang="IN" style="font-family: Wingdings; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-char-type: symbol; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-symbol-font-family: Wingdings;">à</span><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;">wesel yang tidak berbunga<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 150%;"><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;">Wesel dapat dijual sebelum tanggal jatuh temponya tiba.</span><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%; mso-ansi-language: EN-US;"> </span><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: 150%;"><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;"><br /></span></div><div class="MsoNormal" style="line-height: 150%;"><span lang="IN" style="font-family: 'Times New Roman', serif; line-height: 150%;"> </span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">Dalam</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;"> </span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">akuntansi</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">, </span><span style="font-family: 'Century Schoolbook'; font-style: italic; font-weight: bold; text-align: justify; text-indent: -0.5in;">promissory notes</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;"> </span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">juga</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;"> </span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">disebut</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;"> </span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">wesel</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;"> </span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">tagih</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;"> (</span><span style="font-family: 'Century Schoolbook'; font-style: italic; font-weight: bold; text-align: justify; text-indent: -0.5in;">notes receivable</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">) </span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">untuk</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;"> yang </span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">menerima</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;"> </span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">dan</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;"> </span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">wesel</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;"> </span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">bayar</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;"> (</span><span style="font-family: 'Century Schoolbook'; font-style: italic; font-weight: bold; text-align: justify; text-indent: -0.5in;">notes payable</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">) </span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">untuk</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;"> yang </span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">membuat</span><span style="font-family: 'Century Schoolbook'; text-align: justify; text-indent: -0.5in;">.</span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: justify; text-justify: inter-ideograph; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook'; font-size: 20pt;"></span></div><div class="MsoNormal" style="line-height: 150%;"><span lang="IN" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 150%;"><b>Contoh :</b><o:p></o:p></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: justify; text-justify: inter-ideograph; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';">Contoh</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">Soal</span><span style="font-family: 'Century Schoolbook';">:</span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: justify; text-justify: inter-ideograph; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';">Wesel </span><span style="font-family: 'Century Schoolbook';">yang </span><span style="font-family: 'Century Schoolbook';">ditandatangani</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">Marpho’ah</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">dengan</span><span style="font-family: 'Century Schoolbook';"> nominal </span><span style="font-family: 'Century Schoolbook';">Rp</span><span style="font-family: 'Century Schoolbook';">. 200.000.000,- </span><span style="font-family: 'Century Schoolbook';">tanggal</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">penerbitan</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">wesel</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">tanggal</span><span style="font-family: 'Century Schoolbook';"> 1 </span><span style="font-family: 'Century Schoolbook';">Agustus</span><span style="font-family: 'Century Schoolbook';"> 2012 </span><span style="font-family: 'Century Schoolbook';">dan</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">jatuh</span><span style="font-family: 'Century Schoolbook';"> tempo </span><span style="font-family: 'Century Schoolbook';">dalam</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">waktu</span><span style="font-family: 'Century Schoolbook';"> 60 </span><span style="font-family: 'Century Schoolbook';">hari</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">atau</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">tanggal</span><span style="font-family: 'Century Schoolbook';"> 30 September 2012. </span><span style="font-family: 'Century Schoolbook';">Dengan</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">bunga</span><span style="font-family: 'Century Schoolbook';"> 12%. </span><span style="font-family: 'Century Schoolbook';">Maka</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">nilai</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">wesel</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">pada</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">saat</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">jatuh</span><span style="font-family: 'Century Schoolbook';"> tempo </span><span style="font-family: 'Century Schoolbook';">adalah</span><span style="font-family: 'Century Schoolbook';">:</span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: justify; text-justify: inter-ideograph; unicode-bidi: embed; word-break: normal;"><br /></div><div class="MsoNormal" style="line-height: 150%;"></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';"></span></div><ol start="1" style="margin-top: 0mm;" type="a"></ol><br /><div class="MsoNormal" style="line-height: 150%;"><b><span lang="IN" style="font-family: 'Times New Roman', serif; line-height: 150%;">Jawab:<br /></span></b></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: justify; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook'; font-weight: bold;">S  = P ( 1 + </span><span style="font-family: 'Century Schoolbook'; font-weight: bold;">dt</span><span style="font-family: 'Century Schoolbook'; font-weight: bold;">)</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: justify; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';">    = </span><span style="font-family: 'Century Schoolbook';">Rp</span><span style="font-family: 'Century Schoolbook';">. 200.000.000     1 + 0,12 </span><span style="font-family: 'Century Schoolbook';">(</span><span style="font-family: Candara;">60/365</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">)</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: justify; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';">  = </span><span style="font-family: 'Century Schoolbook';">Rp</span><span style="font-family: 'Century Schoolbook';">. 200.000.000     1 + 0,12 (0,164)</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: justify; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">  = </span><span style="font-family: 'Century Schoolbook';">Rp</span><span style="font-family: 'Century Schoolbook';">. 200.000.000 (1,019)</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: justify; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';">  = </span><span style="font-family: 'Century Schoolbook';">RP. 203.945.205,-</span></div><div class="MsoNormal" style="line-height: 150%;"><span lang="IN" style="font-family: 'Times New Roman', serif; line-height: 150%;"><br /><o:p></o:p></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';">Rp</span><span style="font-family: 'Century Schoolbook';">. 200.000.000 (</span><span style="font-family: 'Century Schoolbook';">duaratus</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">juta</span><span style="font-family: 'Century Schoolbook';"> rupiah)                                        </span><span style="font-family: 'Century Schoolbook';">Malang</span><span style="font-family: 'Century Schoolbook';">, 1 </span><span style="font-family: 'Century Schoolbook';">Agustus</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">2012</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';"></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: center; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';">  </span><span style="font-family: 'Century Schoolbook';">Enam</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">puluh</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">hari</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">terhitung</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">dari</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">hari</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">ini</span><span style="font-family: 'Century Schoolbook';">, </span><span style="font-family: 'Century Schoolbook';">saya</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">berjanji</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">untuk</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">membayar</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">kepada</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">Pharel</span><span style="font-family: 'Century Schoolbook';"></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: center; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';"></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: center; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';">Duaratus</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">Juta</span><span style="font-family: 'Century Schoolbook';"> Rupiah</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibYoYARy2M0PPdM7zeApMhyphenhyphenVZ9JEaJ4XZvfjTIeYHIYKrpZ4RvfwO-wMCFF5GafmXKYj5QTq1yjiae28ByymAwBU5DPu3Epk1JjRptF-Bk3vJ_C4uz8Kulxneh_pthtsPGx-UE8wogiVw/s1600/grafik+wesel+1.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;">         </a></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: center; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';">Beserta</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">bunga</span><span style="font-family: 'Century Schoolbook';"> 12% </span><span style="font-family: 'Century Schoolbook';">p.a</span><span style="font-family: 'Century Schoolbook';"></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: right; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';">Tanda</span><span style="font-family: 'Century Schoolbook';"> </span><span style="font-family: 'Century Schoolbook';">Tangan</span><span style="font-family: 'Century Schoolbook';">,</span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: right; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';">     </span><span style="font-family: 'Century Schoolbook';">Marpho’ah</span><span style="font-family: 'Century Schoolbook';"></span><br /><span style="font-family: 'Century Schoolbook';"><br /></span><span style="font-family: 'Century Schoolbook';">baca juga <a href="http://www.allmipa.com/2015/12/matematika-keuangan-diskon-tunai.html" target="_blank"><span style="color: blue;"><b>diskon tunai</b></span></a></span></div><div class="MsoNormal" style="line-height: 150%;"><span lang="IN" style="font-family: 'Times New Roman', serif; line-height: 150%;">   </span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: 'Century Schoolbook';"></span></div></div>

Perhatikan gambar diamping. Ya benar, Gambar kuning yang terpapar tersebut bukan sesuatu yang asing bagi kalian, itulah yang namanya wesel. Wesel merupakan salah satu layanan PT. Pos Indonesia, yang m...

23Dec2015

Sifat-sifat Relasi

December 01, 2015 antisymetric , menghantar , refleksif , relasi , setangkup , sifat , symetric , tolak-setangkip , transitive

<div dir="ltr" style="text-align: left;" trbidi="on"><div class="MsoNormal" style="text-align: justify; text-indent: -37.7953px;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5sken7u0LRixePGMWvhIbQCYDpYdeATVIW_tQ9ZdzI6Xp1hysHtdJP9TLEisdJoPJeD56SmAdosyUucmvNd87uGDpcisLsDLjrGmw801Qt-sb2XXXkWUtfTc9EnsgOaY0yP6jRPsgMKE/s1600/relasi.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="208" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5sken7u0LRixePGMWvhIbQCYDpYdeATVIW_tQ9ZdzI6Xp1hysHtdJP9TLEisdJoPJeD56SmAdosyUucmvNd87uGDpcisLsDLjrGmw801Qt-sb2XXXkWUtfTc9EnsgOaY0yP6jRPsgMKE/s320/relasi.jpg" width="320" /></a></div><div class="MsoNormal" style="text-align: justify;"><span style="text-indent: -10mm;"><span style="font-family: "arial" , sans-serif;">Gambar disamping memberikan suatu wacana pembelajaran, apa yang anda pikirkan? ya, gambar disamping memperlihatkan bahwa terdapat suatu hubungan yang saling berkaitan terhadap orang yang berwarna merah berada di tengah orang-orang dan dihubungkan oleh garis yang saling berhubungan,.</span></span></div><div class="MsoNormal" style="text-align: justify; text-indent: -37.7953px;"><span style="font-family: "arial" , sans-serif;">         Garis besar Illustrasi gambar itu kesimpulannya adalah contoh nyata dari suatu materi matematika yang dinamakan <i>Relasi</i></span></div><div class="MsoNormal" style="text-align: justify;"><span style="text-indent: -10mm;"><span style="font-family: "arial" , sans-serif;"><br /></span></span></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;"><b style="text-indent: -10mm;"><span style="font-family: "arial" , sans-serif;"><u>Refleksif (<i>Reflexive</i>)</u></span></b></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><b><span style="font-family: "arial" , sans-serif;"><i>Definisi :</i></span></b><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><i><span style="font-family: "arial" , sans-serif;">Relasi R pada himpunan A disebut refleksif jika (a,a) </span></i><i><span style="font-family: "symbol";">Î</span></i><i><span style="font-family: "arial" , sans-serif;"> R untuk setiap a </span></i><i><span style="font-family: "symbol";">Î</span></i><i><span style="font-family: "arial" , sans-serif;"> A</span></i></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Definisi di atas menyatakan bahwa di dalam relasi refleksif setiap elemen di dalam A berhubungan dengan dirinya sendiri. Juga menyatakan bahwa relasi R pada himpunan A tidak refleksif jika ada a </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> A tetapi tidak terdapat (a,a).</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /><a name='more'></a><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><span style="font-family: "arial" , sans-serif;"><i>Contoh 1 :</i></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><span style="font-family: "arial" , sans-serif;">Misalkan A = {1, 2, 3, 4} dan relasi R di bawah ini didefinisikan pada himpunan A, maka :</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">Relasi R = { (1,1), (1,3), (2,1), (2,2), (3,3), (4,2), (4,3), (4,4) } bersifat refleksif karena terdapat elemen relasi yang berbentuk (a,a) yaitu (1,1), (2,2), (3,3), dan (4,4)</span></div><div class="MsoNormalCxSpMiddle" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">Relasi R = {(1,1), (2,2), (2,3), (4,2), (4,3), (4,4)} tidak bersifat refleksif karena tidak terdapat (3,3).</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;"><i>Contoh 2 :</i></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Relasi “habis membagi” pada himpunan bilangan bulat positif bersifat refleksif karena setiap bilangan bulat posifit selalu habis membagi dirinya sendiri, sehingga (a,a) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> R untuk setiap a </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> A.</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;"><i>Contoh 3 :</i></span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><span style="font-family: "arial" , sans-serif;">Tiga buah relasi di bawah ini menyatakan relasi pada himpunan bilangan bulat positif</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify; text-indent: 36pt;"><span style="font-family: "arial" , sans-serif;">R : x lebih besar dari y</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify; text-indent: 36pt;"><span style="font-family: "arial" , sans-serif;">S : x + y = 5</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify; text-indent: 36pt;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify; text-indent: 36pt;"><span style="font-family: "arial" , sans-serif;">T : 3x + y = 10</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Mana diantara ketiga relasi tersebut yang bersifat refleksif ?</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><b style="text-indent: -10mm;"><span style="font-family: "arial" , sans-serif;">Setangkup (Symmetric) dan Tolak-Setangkup (Antisymmetric)</span></b></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><b style="text-indent: -10mm;"><span style="font-family: "arial" , sans-serif;"><br /></span></b></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><i style="font-family: Arial, sans-serif;">Definisi Setangkup (Symmetric) </i><b style="font-family: Arial, sans-serif;">:</b></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><i><span style="font-family: "arial" , sans-serif;">Relasi R pada himpunan A disebut setangkup jika (a,b) </span></i><i><span style="font-family: "symbol";">Î</span></i><i><span style="font-family: "arial" , sans-serif;"> R, maka (b,a) </span></i><i><span style="font-family: "symbol";">Î</span></i><i><span style="font-family: "arial" , sans-serif;"> R , untuk a,b </span></i><i><span style="font-family: "symbol";">Î</span></i><i><span style="font-family: "arial" , sans-serif;"> A</span></i></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><span style="font-family: "arial" , sans-serif;">Definisi di atas menyatakan bahwa relasi R pada himpunan A tidak setangkup jika (a,b) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> R sedemikian sehingga (b,a) </span><span style="font-family: "symbol";">Ï</span><span style="font-family: "arial" , sans-serif;"> R.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;"><i>Contoh :</i></span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><span style="font-family: "arial" , sans-serif;">Misalkan A adalah himpunan mahasiswa Teknik Informatika STIKOM Poltek Cirebon dan R adalah relasi pada A sedemikian sehingga (a,b) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> R jika dan hanya jika a satu jurusan dengan b.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Maka jika dibalik, b pun se-jurusan dengan a. Jadi bisa dikatakan bahwa R setangkup.</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><i style="font-family: Arial, sans-serif;">Contoh lain :</i></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><span style="font-family: "arial" , sans-serif;">Misalkan T adalah relasi pada himpunan bilangan bulat positif  sedemikian sehingga (a,b) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> T jika dan hanya jika a </span><span style="font-family: "symbol";">³</span><span style="font-family: "arial" , sans-serif;"> b.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Jelas dong...T tidak setangkup, karena misalnya (6,5) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> T tetapi (5,6) </span><span style="font-family: "symbol";">Ï</span><span style="font-family: "arial" , sans-serif;"> T.</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><b><span style="font-family: "arial" , sans-serif;">Definisi Tolak-Setangkup (antisymmetric) :</span></b></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><i><span style="font-family: "arial" , sans-serif;">Relasi R pada himpunan A disebut tolak-setangkup jika (a,b) </span></i><i><span style="font-family: "symbol";">Î</span></i><i><span style="font-family: "arial" , sans-serif;"> R dan (b,a) </span></i><i><span style="font-family: "symbol";">Î</span></i><i><span style="font-family: "arial" , sans-serif;"> R maka a = b, untuk semua a,b </span></i><i><span style="font-family: "symbol";">Î</span></i><i><span style="font-family: "arial" , sans-serif;"> A.</span></i><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Definisi di atas menyatakan bahwa jika (a,b) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> R, maka (b,a) </span><span style="font-family: "symbol";">Ï</span><span style="font-family: "arial" , sans-serif;"> R kecuali a = b. Juga menyatakan bahwa relasi R pada himpunan A tidak tolak-setangkup jika ada elemen berbeda a dan b  sedemikian  sehingga (a,b) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> R dan (b,a) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> R.</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><i style="font-family: Arial, sans-serif;">Contoh :</i></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><span style="font-family: "arial" , sans-serif;">Misalkan A adalah himpunan tes seleksi yang diadakan untuk masuk bekerja ke sebuah perusahaan (misalnya tes membaca cepat, tes menulis cepat, tes berjalan cepat, dsb).</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Terus.....misalkan R adalah relasi pada A sedemikian sehingga (a,b) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> R jika tes a dilakukan sebelum tes b.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Jadi jelas dong....jika tes a dilakukan sebelum tes b, tes b tidak mungkin dilakukan sebelum tes a untuk dua tes a dan b yang berbeda.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Dengan kata lain, (b,a) </span><span style="font-family: "symbol";">Ï</span><span style="font-family: "arial" , sans-serif;"> R kecuali a = b. Jadi R adalah relasi tolak-setangkup.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><i style="font-family: Arial, sans-serif;">Contoh lagi :</i></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><span style="font-family: "arial" , sans-serif;">Misalkan A = {1,2,3,4} dan relasi R di bawah ini didefinisikan pada himpunan A, maka :</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">Relasi R = {(1,1), (1,2), (2,1), (2,2), (2,4), (4,2), (4,4)} bersifat setangkup karena jika (a,b) </span><span style="font-family: "symbol"; text-indent: -21.3pt;">Î</span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;"> R maka (b,a) juga </span><span style="font-family: "symbol"; text-indent: -21.3pt;">Î</span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;"> R.</span></div><div class="MsoNormalCxSpMiddle" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Disini  (1,2) dan (2,1) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;">R,  begitu  juga  (2,4)  dan  (4,2) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> R.</span></div><div class="MsoNormalCxSpMiddle" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">Relasi R = {(1,1), (2,3), (2,4), (4,2)} tidak setangkup karena (2,3) </span><span style="font-family: "symbol"; text-indent: -21.3pt;">Î</span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;"> R tetapi (3,2) </span><span style="font-family: "symbol"; text-indent: -21.3pt;">Ï</span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;"> R</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">Relasi R = {(1,1), (2,2), (3,3)} tolak-setangkup karena (1,1) </span><span style="font-family: "symbol"; text-indent: -21.3pt;">Î</span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;"> R dan 1 = 1, (2,2) </span><span style="font-family: "symbol"; text-indent: -21.3pt;">Î</span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;"> R dan 2 = 2, (3,3) </span><span style="font-family: "symbol"; text-indent: -21.3pt;">Î</span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;"> R dan 3 = 3.</span></div><div class="MsoNormalCxSpMiddle" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Betulkah bahwa R juga setangkup ??</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">Relasi R = {(1,1), (1,2), (2,2), (2,3)} tolak-setangkup karena (1,1) </span><span style="font-family: "symbol"; text-indent: -21.3pt;">Î</span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;"> R dan 1 = 1, serta (2,2) </span><span style="font-family: "symbol"; text-indent: -21.3pt;">Î</span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;"> R dan 2 = 2.</span></div><div class="MsoNormalCxSpMiddle" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Betulkah bahwa R tidak setangkup ??</span></div><div class="MsoNormalCxSpMiddle" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">Relasi R = {(1,1), (2,4), (3,3), (4,2)} tidak tolak-setangkup karena 2 ≠ 4 tetapi (2,4) dan (4,2) anggota R.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify; text-indent: 0px;"><span style="text-indent: -21.3pt;"><span style="font-family: "times new roman" , serif;">R</span></span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">elasi R = {(1,2), (2,3), (1,3)} tidak setangkup tetapi tolak-setangkup.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><i style="font-family: Arial, sans-serif;">Contoh berikutnya :</i></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">Relasi “habis membagi” pada himpunan bilangan bulat positif dikatakan tidak setangkup karena jika a habis membagi b, b tidak habis membagi a, kecuali jika a = b.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Misalnya, 2 habis membagi 4, tetapi 4 tidak habis membagi 2. Karena itu (2,4) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> R tetapi (4,2) </span><span style="font-family: "symbol";">Ï</span><span style="font-family: "arial" , sans-serif;"> R.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">Relasi “habis membagi” pada himpunan bilangan bulat positif dikatakan tolak-setangkup karena jika a habis membagi b dan b habis membagi a maka a = b.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Misalnya, 4 habis membagi 4 maka oleh karena itu (4,4) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> R dan 4 = 4.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Contoh lagi ??</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;">T</span><span style="font-family: "arial" , sans-serif;">iga buah relasi di bawah ini menyatakan relasi pada himpunan bilanga bulat positif.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">        R : x lebih besar dari y</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">        S : x + y = 6</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">        T : 3x + y = 10</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">R bukan relasi setangkup karena, misalnya 5 lebih besar dari 3, tetapi 3 tidak lebih besar dari 5.</span><span style="font-family: "times new roman" , serif;"> </span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">S relasi setangkup karena, misalnya (4,2) dan (2,4) adalah anggota S.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">T tidak setangkup karena, misalnya (3,1) adalah anggota T tetapi (1,3) bukan anggota T.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">S bukan relasi tolak-setangkup karena, misalnya (4,2) dan (4,2) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> S tetapi 4 ≠ 2.</span><span style="font-family: "times new roman" , serif;"> </span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">R dan T keduanya tolak-setangkup.....buktikan !!!</span><b style="text-indent: -10mm;"><span style="font-family: "times new roman" , serif;"> </span></b></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><b style="text-indent: -10mm;"><span style="font-family: "arial" , sans-serif;"><br /></span></b></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><b style="text-indent: -10mm;"><span style="font-family: "arial" , sans-serif;">Menghantar (transitive)</span></b></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Definisi :</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><i><span style="font-family: "arial" , sans-serif;">Relasi  R  pada  himpunan  A disebut menghantar jika (a,b) </span></i><i><span style="font-family: "symbol";">Î</span></i><i><span style="font-family: "arial" , sans-serif;"> R  dan (b,c) </span></i><i><span style="font-family: "symbol";">Î</span></i><i><span style="font-family: "arial" , sans-serif;"> R, maka (a,c) </span></i><i><span style="font-family: "symbol";">Î</span></i><i><span style="font-family: "arial" , sans-serif;"> R untuk semua a,b,c </span></i><i><span style="font-family: "symbol";">Î</span></i><i><span style="font-family: "arial" , sans-serif;">A</span></i></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Ilustrasinya :</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Misalkan A adalah himpunan orang, dan R adalah relasi pada A sedemikian sehingga (a,b) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> R jika dan hanya jika b adalah keturunan a.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Jika b adalah keturunan a, yaitu (a,b) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> R,  dan c adalah keturunan  b,  yaitu  (b,c) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;">R  maka c juga keturunan a, yaitu (a,c) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> R.</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Jadi, R adalah relasi menghantar. Tetapi, jika T adalah relasi pada A sedemikian sehingga (a,b) </span><span style="font-family: "symbol";">Î</span><span style="font-family: "arial" , sans-serif;"> T jika a adalah ibu dari b, maka T tidak menghantar.</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><i style="font-family: Arial, sans-serif;">Contoh 1 :</i></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Misalkan A = {1,2,3,4}, dan relasi R di bawah ini didefinisikan pada himpunan A, maka :</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">a)</span><span style="font-family: "times new roman" , serif; text-indent: -21.3pt;"> </span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">R = {(2,1), (3,1), (3,2), (4,1), (4,2), (4,3)} bersifat menghantar. Perhatikan tabel berikut :</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><span style="font-family: "arial" , sans-serif;">Pasangan berbentuk</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; margin-left: 26.7pt; text-align: justify;"> <tbody><tr>  <td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(a,b)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td>  <td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(b,c)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td>  <td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(a,c)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td> </tr><tr>  <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(3,2)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td>  <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(2,1)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td>  <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(3,1)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td> </tr><tr>  <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(4,2)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td>  <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(2,1)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td>  <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(4,1)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td> </tr><tr>  <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(4,3)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td>  <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(3,1)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td>  <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(4,1)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td> </tr><tr>  <td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(4,3)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td>  <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(3,2)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td>  <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0mm 5.4pt 0mm 5.4pt; width: 39.55pt;" valign="top" width="53"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: "arial" , sans-serif;">(4,2)</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div></td> </tr></tbody></table><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">b)</span><span style="font-family: "times new roman" , serif; text-indent: -21.3pt;"> </span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">R = {(1,1), (2,3), (2,4), (4,2)} tidak menghantar karena (2,4) dan (4,2) </span><span style="font-family: "symbol"; text-indent: -21.3pt;">Î</span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;"> R, tetapi (2,2) </span><span style="font-family: "symbol"; text-indent: -21.3pt;">Ï</span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">       R, begitu juga (4,2) dan (2,3) </span><span style="font-family: "symbol"; text-indent: -21.3pt;">Î</span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;"> R, tetapi (4,3) </span><span style="font-family: "symbol"; text-indent: -21.3pt;">Ï</span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;"> R.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;"> c)</span><span style="font-family: "times new roman" , serif; text-indent: -21.3pt;">    </span><span style="font-family: "arial" , sans-serif; text-indent: -21.3pt;">R = {(1,1), (2,2), (3,3), (4,4)} jelas menghantar.....buktikan !!!</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;"><i>Contoh 2 :</i></span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Relasi “habis membagi” pada himpunan bilangan bulat positif bersifat menghantar. Misalkan bahwa a habis membagi b dan b habis membagi c. Maka terdapat bilangan positif m dan n sedemikian sehingga b = ma dan c = nb.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Disini c = nma, sehingga a habis membagi c. Jadi, relasi “habis membagi” bersifat menghantar.</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><i><span style="font-family: "arial" , sans-serif;">Contoh 3 :</span></i></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "times new roman" , serif;"> </span><span style="font-family: "arial" , sans-serif;">Tiga buah relasi di bawah ini menyatakan relasi pada himpunan bilangan bulat positif</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">        R : x lebih besar dari y</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">        S : x + y = 6</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">        T : 3x + y = 10</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">R adalah relasi menghantar karena jika x > y dan y > z maka x > z.</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">S tidak menghantar karena, misalkan (4,2) dan (2,4) adalah anggota S tetapi (4,4) </span><span style="font-family: "symbol";">Ï</span><span style="font-family: "arial" , sans-serif;"> S.</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">T tidak menghantar karena, misalkan T = {(1,7), (2,4), (3,1)}</span><span style="font-family: "times new roman" , serif;"><o:p></o:p></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;"><br /></span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-family: "arial" , sans-serif;">Bagaimana kawan, paham bukan penjelasan tentang materi relasi ini? Nah apabila belum paham, janganlah malu-malu untuk bertanya ya kawan! Terima kasih</span></div><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;"><br /></div><br /><div class="MsoNormal" style="text-align: justify;"><br /></div></div>

Gambar disamping memberikan suatu wacana pembelajaran, apa yang anda pikirkan? ya, gambar disamping memperlihatkan bahwa terdapat suatu hubungan yang saling berkaitan terhadap orang yang berwarna mera...

01Dec2015

Lanjutan jawaban soal analisis real 1 (anril) 2.1 no 11-20

December 01, 2015 1 , 2.1 , analisis , anril , jawaban , lanjutan , pembahasan , real , section , Soal

<div dir="ltr" style="text-align: left;" trbidi="on"><div class="MsoNormal" style="text-align: justify;">Jumpa lagi kawan mathers disini kita lanjutkan pembahasan soal analisis real 1 section 2.1 yang akan membahas soal no 11-20. Simak baik-baik ya kawan: </div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;"><b><u>SOAL:</u></b></div><div class="MsoNormal" style="text-align: justify;"><b><u><br /></u></b></div><div class="MsoNormal" style="text-align: justify;">11). a)Tunjukkan bahwa jika a > 0, maka 1/a > 0 dan 1/(1/a) = a<o:p></o:p></div><div class="MsoNormal" style="text-align: justify; text-indent: 14.2pt;"> b) Tunjukkan bahwa jika a < b, maka a < ½ (a + b) < b<o:p></o:p></div><div class="MsoNormal" style="text-align: justify; text-indent: 14.2pt;"><br /></div><div class="MsoNormal" style="text-align: justify;">12). Misalkan <i>a,b,c,d</i> adalah bilangan-bilangan real yang memenuhi <i>0 < a < b dan c < d < 0</i>. Berikan sebuah contoh bilangan-bilangan tersebut yang memenuhi <i>ac < bd</i>. Berikan juga contoh untuk kasus <i>bd < ac</i>,<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;"><br /></div><b style="text-decoration: underline;">Baca juga:</b><b><a href="http://funmathscience.blogspot.co.id/2015/08/cara-menggambar-segi-lima-beraturan.html" target="_blank"> <span style="color: blue;">Cara menggambar segi lima beraturan</span></a></b><br /><b><u><br /></u></b><br /><div class="MsoNormal" style="text-align: justify;">13). Jika  a,b € R, tunjukkan bahwa <i>a<sup>2</sup> + b<sup>2</sup> = 0</i> jika dan hanya jika <i>a = 0</i> dan <i>b = 0</i><o:p></o:p></div><div class="MsoNormal" style="text-align: justify;"><i><br /></i></div><div class="MsoNormal" style="text-align: justify;">14), Jika 0 ≤ a < b tunjukkan bahwa <i>a<sup>2</sup> </i><i>≤</i><i> a b < b<sup>2</sup></i>. Tunjukkan dengan cara memberikan contoh penyangkal bahwa tidak berlaku <i>a<sup>2</sup> < a b < b<sup>2</sup></i>.<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;">15). Jika 0 < a < b, tunjukkan bahwa<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;">       a). a < √ab < b<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;">       b). 1/b < 1/a<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;"><br /><a name='more'></a><br /></div><div class="MsoNormal" style="text-align: justify;">16). Carilah bilangan-bilangan real x yang memenuhi masing-masing pertidaksamaan berikut ini:<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;">        a. x<sup>2</sup> > 3x + 4<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;">        b. 1 < x<sup>2</sup>< 4<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;">        c. 1/x < x<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;">        d. 1/x < x<sup>2</sup><o:p></o:p></div><div class="MsoNormal" style="text-align: justify;"><sup><br /></sup></div><div class="MsoNormal" style="text-align: justify;">17. Buktikan bahwa jika a € R sedemikian hingga <i>0 </i><i>≤</i><i> a </i><i>≤</i><i> </i><i>ԑ</i> untuk setiap <i>ԑ</i> > 0, maka    a = 0<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;">18. Misalkan a, b € Rdan anggap bahwa untuk setiap <i>ԑ > 0</i>, maka a = 0<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;">19. Buktikan bahwa (1/2 (a + b))<sup>2</sup>≤ ½ (a<sup>2</sup> + b<sup>2</sup>) untuk semua a,b € R. Buktikan juga bahwa kesamaan dari bentuk tersebut berlaku jika dan hanya jika a = b.<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;">20. (a) Jika 0 < c < 1, Buktikan bahwa 0 < c<sup>2</sup> < c < 1<o:p></o:p></div><div class="MsoNormal"></div><div class="MsoNormal" style="text-align: justify;">      (b) Jika 1 < c, buktikan bahwa 1 < c < c<sup>2</sup><o:p></o:p></div><div class="MsoNormal" style="text-align: justify;"><sup><br /></sup></div><div class="MsoNormal" style="text-align: justify;"><span style="font-size: 13.3333px;"><b><u>PEMBAHASAN/JAWABAN</u></b></span></div><div class="MsoNormal" style="text-align: justify;"><span style="font-size: 13.3333px;"><b><u><br /></u></b></span></div><div class="MsoNormal" style="text-align: justify;"><div class="separator" style="clear: both; text-align: center;"></div><span style="font-size: 13.3333px;"><span id="goog_1109831006"></span><span id="goog_1109831007"></span>11.) </span><br /><div class="separator" style="clear: both; text-align: center;"><span style="font-size: 13.3333px;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIw2L0vbMp4w7oi6PVxvqyF85ocg7dDjp2M7A7YNP6anzOVSegV6APfH4yvsaSbD4kaG0BZIMKkEQTUP_lS_Ku2tm1oBCpIHeKs_R8M_iD_mMVRHVn4gkKAlzJWMn7wHGbzv0RPOH-5Eg/s1600/jawaban+no+11.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIw2L0vbMp4w7oi6PVxvqyF85ocg7dDjp2M7A7YNP6anzOVSegV6APfH4yvsaSbD4kaG0BZIMKkEQTUP_lS_Ku2tm1oBCpIHeKs_R8M_iD_mMVRHVn4gkKAlzJWMn7wHGbzv0RPOH-5Eg/s1600/jawaban+no+11.jpg" /></a></span></div><div class="separator" style="clear: both; text-align: center;"></div></div><div class="MsoNormal" style="text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoBFjbN5-X8P5TSr6LfPo54qMrx5tgivoj-LAz4ButQgwUS_mdquBWlUG-Jn4BCFPAcKuzhPn4n054jfe1hdGUWwwmpK664HvpKApdzXR9eRycq4mW2CjfdSOrKjJq6vyUUb32ds_caF8/s1600/jawaban+no+11b.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoBFjbN5-X8P5TSr6LfPo54qMrx5tgivoj-LAz4ButQgwUS_mdquBWlUG-Jn4BCFPAcKuzhPn4n054jfe1hdGUWwwmpK664HvpKApdzXR9eRycq4mW2CjfdSOrKjJq6vyUUb32ds_caF8/s1600/jawaban+no+11b.jpg" /></a></div><span style="font-size: 13.3333px;"><b><u><br /></u></b></span></div><div class="MsoNormal" style="text-align: justify;"><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />12,) Jika dipilih a = 2, b = 3, c = -4 dan d = -2, maka kita tahu bahwa 0 < a < b dan c < d < 0. Kemudian perhatikan bahwa: a c = 2 . (-4) = -8 < -6 = 3 . (-2) = bd. Jika dipilih a = 1/2 , b = 6, c = -2 dan d = -1/2, maka kita tahu bahwa 0 < a < b dan c < d < 0, kemudian perhatikan bahwa: b d = 6 . (1/2) = -3 < -1 = ½ . (-2) = ac<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;">13.)<u style="font-weight: bold;"> Bukti ke kanan<o:p></o:p></u></div><div class="MsoNormal" style="text-align: justify;">Jika a, b € R yang memenuhi a<sup>2</sup>+ b<sup>2</sup> = 0, maka a = 0 dan b = 0. Kita akan membuktikan kontraposiisi dari implikasi tersebut benar. Anggap bahwa a ≠ 0 adalah sebarang bilangan real, maka kita tahu bahwa a<sup>2</sup> > 0. Sekarang misalkan b adalah sebarang bilangan real yang lain. Jika b = 0, maka a<sup>2</sup> + b<sup>2</sup> = a<sup>2</sup>+ 0<sup>2</sup> = a<sup>2</sup> > 0. Jadi, jika a ≠ 0 atau b ≠ 0, maka a<sup>2</sup> + b<sup>2</sup>≠ 0<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;"><b><u>Bukti ke Kiri<o:p></o:p></u></b></div><div class="MsoNormal" style="text-align: justify;"></div><div class="MsoNormal" style="text-align: justify;">Jika a = 0 dan b = 0, maka a<sup>2</sup> + b<sup>2</sup> = 0<sup>2</sup> + 0<sup>2</sup> = 0<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;">14.) Jika 0 ≤ a < b, maka a € <b>P</b> U { 0 }, b € <b><span style="font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US;">P </span></b>dan b – a<b></b><b>€</b><b> P. </b>Kemudian a b – a<sup>2</sup> = a (b – a) €<b> P </b>U {0} hal ini berarti a<sup>2</sup> ≤ ab. Selanjutnya, b<sup>2</sup> – ab = b (b – a) €<b> P</b> hal ini berarti ab < b<sup>2</sup>. Jadi dapat disimpulkan a<sup>2</sup>≤ ab < b<sup>2</sup>. Dengan memilih a = 0 dan b = 2, kita tahu bahwa 0 ≤ a < b, namun tidak benar bahwa a<sup>2</sup> < ab, mengingat a<sup>2</sup> = 0 = 0 . 2 = ab.<o:p></o:p></div><div class="MsoNormal" style="text-align: justify;"><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBpeCickpHlGKW0-_LZ2GoUijlg-e5OZEwMVxSdE2_hrinEtFXHhhJq317Cc6lA-nvCSWUWAHhZ1MfgSPVY-NLZD3emGOwktMIb5khDmQyIpbhHj4fiF5Hi6e8Zd-e-TxuM8faAbCtygk/s1600/jawaban+no+15.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBpeCickpHlGKW0-_LZ2GoUijlg-e5OZEwMVxSdE2_hrinEtFXHhhJq317Cc6lA-nvCSWUWAHhZ1MfgSPVY-NLZD3emGOwktMIb5khDmQyIpbhHj4fiF5Hi6e8Zd-e-TxuM8faAbCtygk/s1600/jawaban+no+15.jpg" /></a></div><br /></div><div class="MsoNormal" style="text-align: justify;"><br /><br /><br /><br /><br /><br />16. (a) { x : x < - 1 atau x > 4}<o:p></o:p></div><div class="MsoNormal" style="text-align: justify; text-indent: 14.2pt;"> (b) {x : 1 < x < 2 atau -2 < x < -1}<o:p></o:p></div><div class="MsoNormal" style="text-align: justify; text-indent: 14.2pt;"> (c) {x : -1 < x < 0 atau x > 1}<o:p></o:p></div><div class="MsoNormal" style="text-align: justify; text-indent: 14.2pt;"> (d) { x : x < 0 atau x > 1}<o:p></o:p></div><div class="MsoNormal"></div><div class="MsoNormal" style="text-align: justify;">17. Anggap bahwa a € R sedemikian hingga 0 ≤ a ≤ <i>ԑ</i>, untuk semua <i>ԑ</i> > 0. Andaikan bahwa a > 0, selanjutnya jika dipilih <i>ԑ</i><sub>0</sub> = ½ a > 0, maka 0 < <i>ԑ<sub>0</sub></i> = ½ a < a. hal ini berkontradiksi dengan hipotesis yang mengatakan bahwa 0 ≤ a ≤ <i>ԑ</i>, untuk semua <i>ԑ</i> > o. jadi haruslah a = 0.<o:p></o:p><br /><br /></div><div class="MsoNormal" style="text-align: justify;">18.)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0lNZoDHTnNoYeJSMCY0JgXJKQwmdh86EFoxk5ik_rsYJqAs0MNG-k5dEncA58zMpfkkfErKsIWV5ODON2Ijvs0MhL4pZJZtpkQi6hgUAjzJ0_vxOiXl3KLQGvgXXf4j2I1I3imgrjPL4/s1600/jawaban+no+18.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0lNZoDHTnNoYeJSMCY0JgXJKQwmdh86EFoxk5ik_rsYJqAs0MNG-k5dEncA58zMpfkkfErKsIWV5ODON2Ijvs0MhL4pZJZtpkQi6hgUAjzJ0_vxOiXl3KLQGvgXXf4j2I1I3imgrjPL4/s1600/jawaban+no+18.jpg" /> </a></div><br /></div><div class="MsoNormal" style="text-align: justify;"><br /><br /><br /><br />19.)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7tp01n23zz5qvBaLv_FWdigOHQnjdH9Ehn6zr-aF6OCG3gn0gKnGp8Ba2g7sQzvE7kOkSBQ1UwThZo-2FJdclXyqUbZ49D6DSVl7wtRrpSe6IBcX5Ycyy7b2_4xZ95TdX1HMSyp4HmC4/s1600/jawaban+no+19.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7tp01n23zz5qvBaLv_FWdigOHQnjdH9Ehn6zr-aF6OCG3gn0gKnGp8Ba2g7sQzvE7kOkSBQ1UwThZo-2FJdclXyqUbZ49D6DSVl7wtRrpSe6IBcX5Ycyy7b2_4xZ95TdX1HMSyp4HmC4/s1600/jawaban+no+19.jpg" /></a></div><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />20.) (a) Jika 0 < c < 1, maka 1 – c > 0, lalu kita dapatkan c – c<sup>2</sup> = c (c – 1) > 0. Hal ini berarti c <sup>2</sup> < c. Selanjutnya karena kita tahu bahwa c<sup>2</sup> > 0 dan c < 1, maka kita dapat simpulkan bahwa </div><div class="MsoNormal" style="text-align: justify;">0 < c<sup>2</sup> < c < 1.<o:p></o:p></div><div class="MsoNormal"></div><div class="MsoNormal" style="text-align: justify;">(b) Jika 1 < c, maka c – 1 > 0 dan c > 0, selanjutnya kita dapatkan bahwa c<sup>2</sup> – c = c (c – 1) > 0. Hal ini berarti bahwa c < c<sup>2</sup>. Karena 1 < c dan c < c<sup>2</sup>, maka dapat disimpulkan bahwa 1 < c < c<sup>2</sup>.<o:p></o:p><br /><br />Bagaimana kawan sudah tambah wawasan lagi kan tentang materi analisis real 1 ini? pastinya sudah. nah untuk memperdalam lagi tunggu postingan-postingan tentang anril selanjutnya. Terima kasih atas kunjungannya. </div></div>

Jumpa lagi kawan mathers disini kita lanjutkan pembahasan soal analisis real 1 section 2.1 yang akan membahas soal no 11-20. Simak baik-baik ya kawan: SOAL:11). a)Tunjukkan bahwa jika a > 0, maka 1/a ...

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December 2015

Matematika Keuangan: Diskon Tunai

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Lanjutan jawaban soal analisis real 1 (anril) 2.1 no 11-20

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