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.
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StatementDe 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 Classification
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Source De Morgan's laws - Wikipedia
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Source De Morgan's laws - Wikipedia
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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.
- In Branch: Logic and Foundations, Lead sentence
In Group: Mathematical Logic and Model Theory, Lead section
In propositional logic and Boolean algebra, De Morgan's laws, also known
Proved By: Augustus De Morgan, Lead
They are named after Augustus De Morgan, a 19th-century British mathematician.
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