De Morgan's law

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

Noun

 * 1)  Either of two laws in formal  which state that:
 * 2) The  of a  is the  of the negations; expressed in propositional logic as: ¬ (𝑝 ∧ 𝑞) ⇔ (¬ 𝑝) ∨ (¬ 𝑞)
 * 3) The negation of a disjunction is the conjunction of the negations; expressed in propositional logic as: ¬ (𝑝 ∨ 𝑞) ⇔ (¬ 𝑝) ∧ (¬ 𝑞)
 * 4)  Either of two laws in  which state that:
 * 5) The  of a  is the  of the complements; as expressed by: (𝐴 ∪ 𝐵)′ = 𝐴′ ∩ 𝐵′
 * 6) The complement of an intersection is the union of the complements; as expressed by: (𝐴 ∩ 𝐵)′ = 𝐴′ ∪ 𝐵′
 * 7)  Any of various laws similar to De Morgan’s laws for set theory and logic; for example: ¬∀𝑥 𝑃(𝑥) ⇔ ∃𝑥 ¬𝑃(𝑥)
 * 1)  Any of various laws similar to De Morgan’s laws for set theory and logic; for example: ¬∀𝑥 𝑃(𝑥) ⇔ ∃𝑥 ¬𝑃(𝑥)

Translations

 * Czech: De Morganův zákon
 * Dutch: wet van De Morgan
 * Finnish: De Morganin laki
 * German: De Morgen'sches Gesetz
 * Hebrew:
 * Polish: prawo De Morgana


 * Czech: De Morganův zákon
 * Dutch: wet van De Morgan
 * Finnish: De Morganin laki
 * German: De Morgen'sches Gesetz
 * Hebrew:
 * Polish: prawo De Morgana