De Morgan's laws
or De Mor·gan's law
[ dih mawr-guh nz lawz or dih mawr-guh nz law ]
/ dɪ ˈmɔr gənz ˈlɔz or dɪ ˈmɔr gənz ˈlɔ /
(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. 2019
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
Word Origin for De Morgan's laws
named after Augustus De Morgan (1806–71), British mathematician
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012