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108 lines
5.4 KiB
HTML
108 lines
5.4 KiB
HTML
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<title>Implication and Iff</title>
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<meta name="description" content="Implication says if ... then. Iff says if and only if" />
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<h1 align="center">Implication and Iff</h1>
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<p align="center">The Symbols are <img src="../images/symbols/symbol-implies.gif" alt="implies symbol" width="26" height="20" align="absmiddle" /> and <img src="../images/symbols/symbol-iff.gif" alt="iff symbol" width="42" height="20" align="absmiddle" /></p>
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<h2>Implication: <img src="../images/symbols/symbol-implies.gif" alt="implies symbol" width="26" height="20" align="absmiddle" /></h2>
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<p>Implication says "if ... then"</p>
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<div class="example">
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<h3>Example: </h3>
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<p align="center"><span class="large">If</span> both a and b are odd numbers <span class="large">then</span> (a+b) is even</p>
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<p>can be written as:</p>
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<p align="center">both a and b are odd numbers <img src="../images/symbols/symbol-implies.gif" alt="implies symbol" width="26" height="20" align="absmiddle" /> (a+b) is even</p>
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</div><br />
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<p>The reason it points to the right is that it might not be true the other way</p>
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<div class="example">
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<h3>Example: </h3>
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<p>Just because (a+b) is even does not mean that a and b are odd (they may both be even)</p>
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</div>
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<p> </p>
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<h2>Iff: <img src="../images/symbols/symbol-iff.gif" alt="iff symbol" width="42" height="20" align="absmiddle" /></h2>
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<p>Iff says "if and only if"</p>
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<p>It is an implication that goes <b>both ways</b>.</p>
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<div class="example">
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<h3>Example: </h3>
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<p class="center larger"><span class="larger">x + y = 3</span> <img src="../images/symbols/symbol-iff.gif" alt="iff symbol" width="42" height="20" align="absmiddle" /><span class="larger"> x = 3 − y</span></p>
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<p>That one is true both ways!</p>
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</div>
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<div class="example">
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<h3>Example: </h3>
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<p><b>a</b> and <b>b</b> are both integers. </p>
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<p>If one of <b>a</b> and <b>b</b> is odd and the other is even <span class="large">then</span> (<b>a+b</b>) is odd can be written as: </p>
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<p class="center larger">One of <b>a</b> and <b>b</b> is odd and the other is even <img src="../images/symbols/symbol-iff.gif" alt="iff symbol" width="42" height="20" align="absmiddle" /> (<b>a+b</b>) is odd</p>
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<p> In this case it goes both ways, because if (<b>a+b</b>) is odd and <b>a</b> and <b>b</b> are both integers, then one of them must be odd and the other even.</p>
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<p> </p>
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<div class="related"><a href="index.html">Algebra Index</a></div>
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