# De Morgan's laws

[ dih mawr-guhnz lawz ]

/ dɪ ˈmɔr gənz ˈlɔz /

### noun

(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 states that the complement of the union of two sets is equal to the intersection of the complements of the sets and that the complement of the intersection of two sets is equal to the union of the complements of the sets.

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Also De Mor·gan's law [dih mawr-guhnz law] /dɪ ˈmɔr gənz ˈlɔ/ .

## Origin of De Morgan's laws

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

## Words nearby De Morgan's laws

demonstrative pronouns, demonstrator, demonym, demoralize, De Morgan, De Morgan's laws, demos, demoscene, Demosthenes, demote, demothball

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2021

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## British Dictionary definitions for De Morgan's laws

De Morgan's laws

### pl n

(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

## Word Origin for De Morgan's laws

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

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
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