Union

From CS2800 wiki


Definition: Union
If [math]A [/math] and [math]B [/math] are sets, then the union of [math]A [/math] and [math]B [/math] (written [math]A \href{/cs2800/wiki/index.php/%5Ccup}{\cup} B [/math]) is given by [math]A \cup B \href{/cs2800/wiki/index.php/Definition}{:=} \{x \href{/cs2800/wiki/index.php/%5Cmid}{\mid} x \href{/cs2800/wiki/index.php/%5Cin}{\in} A \href{/cs2800/wiki/index.php/Or}{\text{ or }} x \href{/cs2800/wiki/index.php/%5Cin}{\in} B\} [/math].

This means that if you know [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} A \href{/cs2800/wiki/index.php/%5Ccup}{\cup} B [/math], you can conclude that 'either' [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} A [/math] 'or' [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} B [/math], and similarly you can prove [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} A \href{/cs2800/wiki/index.php/%5Ccup}{\cup} B [/math] if you can either prove [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} A [/math] or that [math]x \href{/cs2800/wiki/index.php/%5Cin}{\in} B [/math].

In this Venn diagram, the union of [math]A [/math] and [math]B [/math] is shaded:

Venn-union.svg