Set difference

Let $A$ and $B$ be sets . The set difference (or relative complement) of $B$ in $A$ is

Set difference can be expressed using intersection and a complement when a universe is fixed, and it is a basic operation in describing subsets and partitions .

Examples:

• $\{1,2,3\} \setminus \{2\} = \{1,3\}$.
• $(0,2)\setminus(1,3) = (0,1]$.
• If $A \subseteq B$ (see subset ), then $A\setminus B = \emptyset$.