# De Morgan's laws

### or De Mor·gan's law

[dih mawr-guh nz lawz or dih mawr-guh nz law]

- (used with a plural verb) Logic. two laws, one stating that the denial of the conjunction of a class of propositions is equivalent to the disjunction of the denials of a proposition, and the other stating that the denial of the disjunction of a class of propositions is equivalent to the conjunction of the denials of the propositions.
- (used with a singular verb) Mathematics.
- the theorem of set theory that the complement of the union of two sets is equal to the intersection of the complements of the sets.
- the theorem of set theory that the complement of the intersection of two sets is equal to the union of the complements of the sets.

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## Origin of De Morgan's laws^{}

First recorded in 1915–20; named after A. De Morgan

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## De Morgan's laws

- (in formal logic and set theory) the principles that conjunction and disjunction, or union and intersection, are dual. Thus the negation of P & Q is equivalent to not-P or not-Q

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## Word Origin

named after Augustus De Morgan (1806–71), British mathematician

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
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