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Complement (set theory)

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In set theory, the complement of a set A is the set of all elements that are not in A .

Absolute complement

If the universal set U is defined, then, in terms of the relative complement, the complement of A is

A^C=U\setminus A

Relative complement

Given two sets A,B , the relative complement of A in B , denoted as A\setminus B (sometimes A-B) is

A\setminus B=\{x|x\in B\and x\in A\}

Example

  1. Suppose the universe U is the set of all letters in the English alphabet. The complement of the set of all vowels in U , V^C (V being the set), is the set of all consonants.

See also

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