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De Morgan's laws

or De Mor·gan's law

[dih mawr-guh nz lawz or dih mawr-guh nz law]
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noun
  1. (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.
  2. (used with a singular verb) Mathematics.
    1. 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.
    2. 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

British Dictionary definitions for de morgan's laws

De Morgan's laws

pl n
  1. (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 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012