Prove or Disprove that if q² is even then q is even

StudyBlue printing of Prove or Disprove that if q² is even then q is even html, body, div, span, applet, object, iframe, h1, h2, h3, h4, h5, h6, p, blockquote, pre, a, abbr, acronym, address, big, cite, code, del, dfn, em, font, img, ins, kbd, q, s, samp, small, strike, strong, sub, sup, tt, var, b, u, i, center, fieldset, form, label, legend, table, caption, tbody, tfoot, thead, tr, th, td { margin: 0; padding: 0; border: 0; outline: 0; font-size: 100%; background: transparent; } body { line-height: 1; } blockquote, q { quotes: none; } blockquote:before, blockquote:after, q:before, q:after { content: ''; content: none; } /* remember to define focus styles! */ :focus { outline: 0; } /* remember to highlight inserts somehow! */ ins { text-decoration: none; } del { text-decoration: line-through; } /* tables still need 'cellspacing="0"' in the markup */ table { border-collapse: collapse; border-spacing: 0; } /* end RESET */ .header { min-width:800px; } .logo { padding:6px 20px 2px 20px; margin:0; font-size:25px; font-weight:bold; color:#808285; position:relative; border-bottom: 1px solid #c5c5c5; } .logo-blue { color:#70adc4; } .logo-desc { font-weight:normal; font-size:19px; color:#cccccc; margin-top:50px; position:absolute; display: none; } .back-button { position:absolute; top:20px; right:20px; font-size:13px; line-height:25px; color:rgb(0,175,225); font-weight:normal; } .back-button a { color:rgb(0,175,225); } .instructions { padding:0; margin:0; width:100%; position:relative; color:rgb(100,100,100); } .step-holder { border-left:1px solid #ededed; margin-left:20px; } .steps { padding:15px 0; float:left; width:24%; border-right:1px solid #ededed; text-align:center; } .steps-01 { } .steps-02 { } .steps-03 { } .steps-04 { } .label { padding:5px 10px; } .print-button { } .print-button a { background-color:rgb(0,175,225); color:white; line-height: 19px; padding:9px 8px 5px 30px; font-size:14px; text-decoration:none; background-image: url(images/printer.png); background-repeat: no-repeat; background-position: 7px 50%; -moz-border-radius: 5px; -webkit-border-radius: 5px; } .print-button a:hover { background-color:black; } .theNote .content { width: 8.0in !important; margin: 5px auto; padding:20px; background-color:white; } .theNote .header { border-bottom: 1px dashed #C8C8C8; font-size: 17px; padding: 0 0 10px; line-height: 19px; color: #00ADE1; min-width:500px; } .theNote .body { font-size: 14px; line-height: 19px; padding: 10px 0; } .theNote{ padding:6px 0; clear:both; background-color: rgb(200,200,200); } .theNote h3{ color: rgb(100,100,100); } .theNote h1, .theNote h3{ background-color:white; padding:2px 20px; width:8.0in !important; margin: 0 auto; font-size: 15px; } .theNote h1{ padding-top: 10px; font-size: 15px; } .theNote h1:first-child{ font-size: 20px; } .theNote h3 { font-size: 14px; font-weight: normal; } #options { border: 3px double #ccc; padding: 5px 12px; margin: 10px 50px 10px 20px; float: left; } #info { border-top: 1px solid #ccc; padding-top: 5px; font-style: italic; } li { margin: 5px 10px 5px 25px; } ul li { list-style: disc; } ol li { list-style: decimal; } img { border: 0; } table { clear: both; width: 100%; border: 1px solid #c5c5c5; border-width: 1px 0; margin: 0; page-break-after: always; } table#page { page-break-after: auto; } td { text-align: center; font-size: 12px; border-bottom: 1px dashed #c5c5c5; height: 1.75in; width: 50%; padding-left: 15px; } .leftside { border-right: 1px solid #cccccc; padding: 0 15px 0 0; } .bottom td { border-bottom: none; } .clearfix { clear:both; line-height:1px; height:1px; } img { max-width:80%; max-height:150px; margin:20px; } @media print {.header { display: none; } .content .header{ display:inherit; } table { border: 1px dashed #bbb; border-width: 1px 0; } .theNote{ background-color:white; } } null q 2 → q where q is even Suppose q is false, hence odd then q = (2k+1) q 2 = (2k+1) 2 = (2k+1)(2k+1) = 4k 2 + 4k + 1 ≡ to false because it is odd q 2 → q q 2 → q so contradiction.. F T T F