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A set theory operator representing the complement of a set relative to the universal set.

\complement image

Examples

Set complement notation

Ac=A=XAA^c = \complement A = X \setminus A
A^c = \complement A = X \setminus A

Complement in probability

P(E)=1P(E)P(\complement E) = 1 - P(E)
P(\complement E) = 1 - P(E)

Set theory with complements

(A)(B)=(AB)(\complement A) \cap (\complement B) = \complement(A \cup B)
(\complement A) \cap (\complement B) = \complement(A \cup B)
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