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292 lines
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Set Symbols</h1>
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<p>A <a href="sets-introduction.html">set</a> is a collection of things, usually numbers. We can list each element (or "member") of a set inside curly brackets like this:</p>
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<p class="center"><img src="images/set.svg" alt="Set Notation" height="118" width="372"></p>
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<h2>Common Symbols Used in Set Theory</h2>
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<p>Symbols save time and space when writing. Here are the most common set symbols</p>
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<p class="center"><i>In the examples C = {1, 2, 3, 4} and
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D = {3, 4, 5}</i></p>
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<div class="beach">
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<table align="center">
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<tbody>
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<tr>
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<th style="width:90px;" align="center">Symbol</th>
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<th align="center">Meaning </th>
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<th>Example</th>
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</tr>
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<tr style="text-align:center;">
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<td class="large">{ }</td>
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<td><a href="sets-introduction.html">Set</a>: a collection of elements</td>
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<td>{1, 2, 3, 4}</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">A <span class="uni">∪</span> B</td>
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<td><a href="venn-diagrams.html">Union</a>: in A or B (or both)</td>
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<td>C <span class="uni">∪</span> D = {1, 2, 3, 4, 5}</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">A <span class="uni">∩</span> B</td>
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<td><a href="venn-diagrams.html">Intersection</a>: in both A and B</td>
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<td>C <span class="uni">∩</span> D = {3, 4}</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">A <span class="uni">⊆</span> B</td>
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<td>Subset: every element of A is in B.<span itemprop="articleBody"></span></td>
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<td>{3, 4, 5} <span class="uni">⊆</span> D</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">A <span class="uni">⊂</span> B</td>
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<td>Proper Subset: every element of A is in B,<br>
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but B has more elements.</td>
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<td>{3, 5} <span class="uni">⊂</span> D</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">A <span class="uni">⊄</span> B</td>
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<td>Not a Subset: A is not a subset of B</td>
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<td>{1, 6}<span class="uni"> ⊄</span> C</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">A <span class="uni">⊇</span> B</td>
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<td> Superset: A has same elements as
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B, or more</td>
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<td>{1, 2, 3}<span class="uni"> ⊇</span> {1, 2, 3}</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">A <span class="uni">⊃</span> B</td>
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<td>Proper Superset: A has B's elements and more</td>
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<td>{1, 2, 3, 4}<span class="uni"> ⊃</span> {1, 2, 3}</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">A <span class="uni">⊅</span> B</td>
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<td>Not a Superset: A is not a superset of B</td>
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<td>{1, 2, 6} <span class="uni">⊅</span> {1, 9}</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">A<sup>c</sup></td>
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<td><a href="venn-diagrams.html">Complement</a>: elements not in A</td>
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<td>D<sup>c</sup> = {1, 2, 6, 7}<br>
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When <img src="../images/symbols/set-u.svg" alt="set universal" height="23" width="24"> = {1, 2, 3, 4, 5, 6, 7}</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">A − B</td>
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<td><a href="venn-diagrams.html">Difference</a>: in A but not in B</td>
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<td>{1, 2, 3, 4}<span> −</span> {3, 4} = {1, 2}</td>
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</tr>
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<tr><th align="center"><br>
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</th><th align="center"><br>
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</th><th><br></th></tr><tr style="text-align:center;">
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<td class="large"><i>a</i> <span class="uni">∈</span> A</td>
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<td><a href="sets-introduction.html">Element</a> of: <i>a</i> is in A</td>
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<td> 3 <span class="uni">∈</span> {1, 2, 3, 4}</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large"><i>b</i> <span class="uni">∉</span> A</td>
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<td>Not element of: <i>b</i> is not in A</td>
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<td>6 <span class="uni">∉</span> {1, 2, 3, 4}</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large bigger">Ø</td>
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<td><a href="sets-introduction.html">Empty set</a> = {}</td>
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<td>{1, 2} <span class="uni">∩</span> {3, 4} = Ø</td>
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</tr>
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<tr style="text-align:center;">
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<td><img src="../images/symbols/set-u.svg" alt="set universal" height="23" width="24"></td>
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<td><a href="sets-introduction.html">Universal Set</a>: set of all possible values<br>
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(in the area of interest)</td>
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<td> </td>
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</tr>
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<tr><th align="center"><br></th><th align="center"><br></th><th><br></th></tr>
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<tr style="text-align:center;">
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<td class="large"><b>P</b>(A)</td>
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<td><a href="power-set.html">Power Set</a>: all subsets of A</td>
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<td>P({1, 2}) = { {}, {1}, {2}, {1, 2} }</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">A = B</td>
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<td>Equality: both sets have the same members</td>
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<td> {3, 4, 5} = {5, 3, 4}</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">A×B</td>
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<td>Cartesian Product<br>
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(set of ordered pairs from A and B)</td>
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<td>{1, 2} × {3, 4}<br>
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= {(1, 3), (1, 4), (2, 3), (2, 4)}</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">|A|</td>
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<td> Cardinality: the number of elements of set A</td>
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<td> |{3, 4}| = 2</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">|</td>
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<td><a href="set-builder-notation.html">Such that</a></td>
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<td> {
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<em>n</em>
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<em>n</em>
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> 0 } = {1, 2, 3,...}</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">:</td>
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<td><a href="set-builder-notation.html">Such that</a></td>
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<td> {
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<em>n</em>
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:
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<em>n</em>
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> 0 } = {1, 2, 3,...}</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">∀</td>
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<td>For All</td>
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<td><span class="uni">∀</span>x>1, x<sup>2</sup>>x<br>
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<span class="says">For all x greater than 1<br>x-squared is greater than x</span>
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</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">∃</td>
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<td>There Exists</td>
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<td><span class="uni">∃</span> x | x<sup>2</sup>>x<br>
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<span class="says">There exists x such that<br>x-squared is greater than x</span>
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</td>
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</tr>
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<tr style="text-align:center;">
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<td class="large">∴</td>
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<td>Therefore</td>
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<td>a=b <span class="uni">∴</span> b=a</td>
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</tr>
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<tr><th align="center"><br></th><th align="center"><br></th><th><br></th></tr>
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<tr style="text-align:center;">
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<td><img src="../images/symbols/set-n.svg" alt="Natural Numbers" style="vertical-align:middle;" height="23" width="25"></td>
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<td><a href="../whole-numbers.html">Natural Numbers</a> </td>
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<td> {1, 2, 3,...} or {0, 1, 2, 3,...}</td>
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</tr>
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<tr style="text-align:center;">
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<td><img src="../images/symbols/set-z.svg" alt="Integers" style="vertical-align:middle;" height="23" width="20"></td>
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<td><a href="../whole-numbers.html">Integers</a></td>
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<td>{..., −3, −2, −1, 0, 1, 2, 3, ...}</td>
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</tr>
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<tr style="text-align:center;">
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<td><img src="../images/symbols/set-q.svg" alt="Rational Numbers" style="vertical-align:middle;" height="31" width="23"></td>
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<td><a href="../rational-numbers.html">Rational Numbers</a></td>
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<td> </td>
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</tr>
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<tr style="text-align:center;">
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<td><img src="../images/symbols/set-a.svg" alt="Algebraic Numbers" style="vertical-align:middle;" height="23" width="25"></td>
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<td><a href="../numbers/algebraic-numbers.html">Algebraic Numbers</a></td>
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<td> </td>
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</tr>
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<tr style="text-align:center;">
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<td><img src="../images/symbols/set-r.svg" alt="Real Numbers" style="vertical-align:middle;" height="23" width="23"></td>
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<td><a href="../numbers/real-numbers.html">Real Numbers</a></td>
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<td> </td>
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</tr>
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<tr style="text-align:center;">
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<td><img src="../images/symbols/set-i.svg" alt="Imaginary Numbers" style="vertical-align:middle;" height="23" width="11"></td>
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<td><a href="../numbers/imaginary-numbers.html">Imaginary Numbers</a></td>
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<td>3<b>i</b></td>
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</tr>
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<tr style="text-align:center;">
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<td><img src="../images/symbols/set-c.svg" alt="Complex Numbers" style="vertical-align:middle;" height="23" width="20"></td>
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<td><a href="../numbers/complex-numbers.html">Complex Numbers</a></td>
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<td>2 + 5<b>i</b></td>
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</tr>
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</tbody></table>
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</div>
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<p> </p>
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<p> </p>
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<div class="related">
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<a href="../algebra/symbols.html">Symbols in Algebra</a>
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<a href="../symbols.html">Symbols in Mathematics</a>
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<a href="index.html">Sets Index</a>
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</div>
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<footer id="footer" class="centerfull noprint"></footer>
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<div id="copyrt">Copyright © 2021 MathsIsFun.com</div>
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