Complement (set theory)

In set theory, the complement of a set $A$ , often denoted by $A^{\complement }$ (or $A'$ ), is the set of elements not in $A$ .

If

A

is the area colored red in this image…

… then the complement of

A

is everything else.

When all elements in the universe, i.e. all elements under consideration, are considered to be members of a given set $U$ , the absolute complement of $A$ is the set of elements in $U$ that are not in $A$ .

The relative complement of $A$ with respect to a set $B$ , also termed the set difference of $B$ and $A$ , written $B\setminus A,$ is the set of elements in $B$ that are not in $A$ .

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