Set difference - Imported Knowlpedia Content

A set difference (or relative complement) of sets $A$ and $B$ is the set

A\setminus B=\{x : x\in A \text{ and } x\notin B\}.

Remarks

Set difference can be expressed using intersection and complement once an ambient universe $U$ is chosen: if $B\subseteq U$ , then $A\setminus B = A\cap B^{c}$ .

Examples

$\{1,2,3\}\setminus\{2,4\}=\{1,3\}$ .
If $A\subseteq B$ , then $A\setminus B=\varnothing$ (see empty set).