Venn diagram lab

<p>A set is a collection of distinct elements. Order does not matter, and repeated entries are counted once. The universal set&nbsp;\(\xi\) specifies all objects under consideration.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center">Notation</th><th style="text-align: center; --cell-justify: center">Meaning</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">\(x\in A\); \(x\notin A\)</td><td style="text-align: center; --cell-justify: center">x is an element of A; x is not an element of A.</td></tr><tr><td style="text-align: center; --cell-justify: center">\(A\subseteq B\)</td><td style="text-align: center; --cell-justify: center">Every element of A is in B; equality is allowed.</td></tr><tr><td style="text-align: center; --cell-justify: center">\(A\subset B\)</td><td style="text-align: center; --cell-justify: center">A is a proper subset of B: every element of A is in B, and A is not B.</td></tr><tr><td style="text-align: center; --cell-justify: center">\(\varnothing\); \(n(A)\)</td><td style="text-align: center; --cell-justify: center">The empty set; the number of elements of A.</td></tr></tbody></table></div></div>
<p>In this chapter, \(\subset\) denotes a proper subset. Compare an element with a set using \(\in\); compare two sets using \(\subseteq\) or \(\subset\). If&nbsp;\(A=\{2,4\}\), then&nbsp;\(2\in A\) and \(\{2\}\subset A\), but \(\{2\}\notin A\).</p>
<p>Set-builder notation gives a rule and a domain. For example, \(\{x\in\mathbb Z:-2\le x&lt;2\}=\{-2,-1,0,1\}\). The set&nbsp;\(\{0\}\) has one element; it is not \(\varnothing\).</p>

A set is a collection of distinct elements. Order does not matter, and repeated entries are counted once. The universal set \(\xi\) specifies all objects under consideration.

In this chapter, \(\subset\) denotes a proper subset. Compare an element with a set using \(\in\); compare two sets using \(\subseteq\) or \(\subset\). If \(A=\{2,4\}\), then \(2\in A\) and \(\{2\}\subset A\), but \(\{2\}\notin A\).

Set-builder notation gives a rule and a domain. For example, \(\{x\in\mathbb Z:-2\le x<2\}=\{-2,-1,0,1\}\). The set \(\{0\}\) has one element; it is not \(\varnothing\).

Elements, subsets and the universal set

Elements, subsets and the universal set

Notation	Meaning
\(x\in A\); \(x\notin A\)	x is an element of A; x is not an element of A.
\(A\subseteq B\)	Every element of A is in B; equality is allowed.
\(A\subset B\)	A is a proper subset of B: every element of A is in B, and A is not B.
\(\varnothing\); \(n(A)\)	The empty set; the number of elements of A.