Set difference

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

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 ).