De Morgan's laws

Noun

De Morgan's law (plural De Morgan's laws)

1. The negation of a conjunction is the disjunction of the negations; expressed in propositional logic as: ¬ (𝑝 ∧ 𝑞) ⇔ (¬ 𝑝) ∨ (¬ 𝑞)
   • Let ‘F’ stand for the state of affairs that consists in finite persons possessing and exercising free will. Let ‘p’ stand for ‘God exists’; ‘q’ for ‘F obtains’; ‘r’ for ‘F poses a serious risk of evil’; and ‘s’ for ‘There is no option available to God that counters F.’ With this in place, the...2004 August, J. L. Schellenberg, “The Atheist’s Free Will Offence”, in International Journal for Philosophy of Religion, volume 56, № 1, pages 11-12
2. The negation of a disjunction is the conjunction of the negations; expressed in propositional logic as: ¬ (𝑝 ∨ 𝑞) ⇔ (¬ 𝑝) ∧ (¬ 𝑞)
3. The complement of a union is the intersection of the complements; as expressed by: (𝐴 ∪ 𝐵)′ = 𝐴′ ∩ 𝐵′
4. The complement of an intersection is the union of the complements; as expressed by: (𝐴 ∩ 𝐵)′ = 𝐴′ ∪ 𝐵′
5. (broadly) Any of various laws similar to De Morgan’s laws for set theory and logic; for example: ¬∀𝑥 𝑃(𝑥) ⇔ ∃𝑥 ¬𝑃(𝑥)