# 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]

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 is the set of elements in B that are not in A.