# de-morgan-s-law

Noun

(*plural* De Morgan's laws)

- (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: ¬ (∨) ⇔ (¬) ∧ (¬)

- (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: (∩)′ = ′ ∪ ′

- (mathematics, loosely) Any of various laws similar to De Morgan’s laws for set theory and logic; for example: ¬∀ ⇔ ∃ ¬

Origin

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