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Complement ○|Definition|1st|20251119205401-00-⌔

Complement (set theory) - Wikipedia

Complement (set theory)

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If A is the area colored red in this image…

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… then the complement of A is everything else.

In set theory, the complement of a set A, often denoted by (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 is the set of elements in B that are not in A.

Printed 2026-06-28.

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Footnotes

  1. “Complement and Set Difference”. web.mnstate.edu. Retrieved 2020-09-04.

  2. “Complement (set) Definition (Illustrated Mathematics Dictionary)”. www.mathsisfun.com. Retrieved 2020-09-04.

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