DS-HTML-Project/properties.html at master · the4thdave/DS-HTML-Project · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <title>Properties of Relations</title>
    <link rel="stylesheet" type="text/css" href="style.css"/>
</head>
<body id="properties">
<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>
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                    <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 - Properties of Relations</h1>
                                <h4>by David Muñoz and Will Ptacek</h4>
                            </div>
                            <div class="ptext">
                                <p><span class="bold">Reflexivity:</span> <br>
                                    When all ordered pairs in a relation have the same element in both positions for
                                    all elements.
                                    <br> In math: for relation r on A, r is
                                    reflexive if:</p>
                                <div class="formula"><span class="formula">(x,x) ∈ r for any x ∈ A</span></div>
                                <p><span class="bold">Symmetry:</span><br>
                                    When a relation has the ordered pair (x,y), it also has the ordered pair (y,x)
                                    <br> In math: for relation r on A, r is symmetric if:</p>
                                <div class="formula"><span class="formula">(x,y) ∈ r => (y,x) ∈ r for any x, y ∈ A</span></div>
                                <p><span class="bold">Transitivity:</span><br>
                                    When a relation has ordered pairs that can be used to equal others; if (x,y) and
                                    (y,z) are in the relation, then (x,z) must also be in the relation. <br>
                                    In math: for relation r on A, r
                                    ⊆ A x A is transitive if:</p>
                                <div class="formula"><span class="formula">(x,y) ∈ r and (y,z) ∈ r => (x,z) ∈ r for any x, y, z ∈ A</span></div>
                                </p>
                            </div>
                        </div>
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