# De-morgan-s-law definition

(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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## Other Word Forms

### Noun

Singular:

de-morgan-s-law
Plural:

de-morgan-s-laws## 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.
### From Wiktionary