De-morgan-s-law meaning

(mathematics, logic) Either of two laws in formal logic which state that:
  • The negation of a conjunction is the disjunction of the negations; expressed in propositional logic as: ¬ (∧) ⇔ (¬) ∨ (¬).
  • The negation of a disjunction is the conjunction of the negations; expressed in propositional logic as: ¬ (∨) ⇔ (¬) ∧ (¬).
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(mathematics) Either of two laws in set theory which state that:
  • The complement of a union is the intersection of the complements; as expressed by: (∪)′ = ′ ∩ ′.
  • The complement of an intersection is the union of the complements; as expressed by: (∩)′ = ′ ∪ ′.
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(mathematics, loosely) Any of various laws similar to De Morgan’s laws for set theory and logic; for example: ¬∀ ⇔ ∃ ¬
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Origin of de-morgan-s-law

Named after its eponym, the British mathematician and logician Augustus De Morgan (1806–1871), who first formulated the laws in formal propositional logic.