# 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 $A^{\complement }$ (or *A*′),^{[1]} is the set of elements not in A.^{[2]}

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.