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DeMorgan's laws are a collection of replacement rules for propositional logic that state that the negation of the conjunction of any two propositions is logically equivalent to the disjunction of the negations of those two propositions. They also state that the negation of the disjunction of any two propositions is logically equivalent to the conjunction of the negations of those propositions[1][2] In symbols:

  • \lnot (A \land B) \Leftrightarrow (\lnot A \lor \lnot B)
  • \lnot (A \lor B) \Leftrightarrow (\lnot A \land \lnot B)

In set theory, it is the rule that the complement of the union of any two sets is equal to the intersection of the complements of those two sets[3]. Also, they state that the complement of the intersection of any two sets is equal to the union of the complements of those sets. In symbols:

  • (A \cup B)^c = (A^c \cap B^c)
  • (A \cap B)^c = (A^c \cup B^c)

ReferencesEdit

  1. DeMorgan's Laws. Whitman College. Web. 4 April 2017. <https://www.whitman.edu/mathematics/higher_math_online/section01.03.html>
  2. DeMorgan's laws { Philosophy Index }. Philosophy Index.Web.4 April 2017. <http://www.philosophy-index.com/logic/forms/de-morgan-laws.php>
  3. Weisstein, Eric W. "de Morgan's Laws." From MathWorld -- A Wolfram Web Resource. Wolfram Research, Inc. Web. 4 April 2017. <http://mathworld.wolfram.com/deMorgansLaws.html>

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