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De Morgan's Laws

Logic and Foundations

In propositional logic and Boolean algebra, De Morgan's laws are a pair of transformation rules that are valid rules of inference, named after the nineteenth century British mathematician Augustus De Morgan. The laws allow conjunctions and disjunctions to be expressed purely in terms of each other through negation: the negation of A and B is the same as not A or not B, and the negation of A or B is the same as not A and not B. The same pattern holds in set theory, where the complement of the union of two sets equals the intersection of their complements.

Facts
Statement
De Morgan's laws are a pair of transformation rules that are both valid rules of inference, allowing conjunctions and disjunctions to be expressed purely in terms of each other via negation. 1
Proof Year
1847 1
Sources
1. De Morgan's laws - Wikipedia
  • Lead paragraph, sentence 1
    In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference.
  • History section
    The first explicit statement of De Morgan's laws in his own work can be found in his 1847 book Formal Logic.
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