# 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: ¬ (∨) ⇔ (¬) ∧ (¬).

noun

(mathematics) Either of two laws in set theory which state that:

- The complement of an intersection is the union of the complements; as expressed by: (∩)′ = ′ ∪ ′.

noun

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

noun

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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.