# Complement (set theory)

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

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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 ${\displaystyle B\setminus A,}$ is the set of elements in B that are not in A.