Complement (set theory)

In set theory, the complement of a set $A$ , often denoted by $A ∁$ (or $A'$ ),[1] is the set of elements not in $A$ .[2]

If

A

is the area colored red in this image…

… then the complement of

A

is everything else.

When all sets in the universe, i.e. all sets 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 $A$ .

Complement (set theory)

Set of the elements not in a given subset / From Wikipedia, the free encyclopedia

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