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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>Examples</title>
<link rel="stylesheet" type="text/css" href="style.css"/>
</head>
<body id="examples">
<div id="wrapper">
<header>
<div class="container clearfix">
<h1>
<a class="gear" href="index.html" title="Home">
<img alt="gear" src="gear.png">
</a>
</h1>
<h1 class="title">Discrete Structures Tutorials</h1>
<nav>
<ul id="topbar">
<li><a class="navlink" href="index.html">Home</a></li>
<li><a class="navlink" href="binary-search.html">Binary Search</a></li>
<li><a class="navlink" href="about.html">About</a></li>
<li><a class="navlink" href="references.html">References</a></li>
</ul>
</nav>
</div>
</header>
<main>
<div class="container">
<div class="row">
<div class="midcolumn">
<aside class="sidebar">
<ul class="mainmenu">
<li class="heading">Content</li>
<li><a class="sidelink" href="relation.html">What is a Relation?</a></li>
<li><a class="sidelink" href="properties.html">Properties of Relations</a></li>
<li><a class="sidelink" href="tables.html">Relations as Tables</a></li>
<li><a class="sidelink" href="graphs.html">Relations as Graphs</a></li>
<li><a class="sidelink" href="examples.html">Examples</a></li>
</ul>
</aside>
</div>
<div class="row">
<div class="content">
<div class="midcolumn2">
<!-- Main Content -->
<div class="heading">
<h1>Relations Tutorial - Examples</h1>
<h4>by David Muñoz and Will Ptacek</h4>
</div>
<div class="ptext">
<p class="lower">Textbook Examples:</p>
<ol class="list2">
<li>In a high school graduation class, (x,y) is in the relation r if person x is the
same height as person y.
Is this reflexive? <br><br>
Yes, (x,x) will always be the same, as person x is always the height of person x.
</li>
<li>In a high school graduation class, (x,y) is in the relation r if person x is the
same age as y.
Is this symmetrical? <br><br>
Yes. If you are the same age as someone else, then they are the same age as you.
</li>
<li>In a high school graduation class, (x,y) is in the relation r if person x is the
same height as person y.
Is this transitive? <br><br>
Yes. If (x,y) are in the relation, then the height of x = the height of y.
If (y,z) is in the relation, that means that the height of y = the height of z.
So, the height of z = the height of x, so it is transitive.
</li>
</ol>
<p>Practice Problems (Try these on your own):</p>
<p>What properties does the equation X ≤ Y have...</p>
<ol class="list">
<li>If x = 3?</li>
<li>If x = 3 and y = 4?</li>
<li>If x = 3 and y = 4 and z = 5?</li>
</ol>
</div>
</div>
<div class="row">
<div class="midcolumn3" id="rightbar"></div>
</div>
</div>
</div>
</div>
</div>
</main>
</div>
</body>
</html>