Word.ws English Dictionary

De Morgan's law

US/dɨˈmɔɹɡɪnzˌlɔ/

De Morgan's law noun: the negation of a conjunction is the disjunction of the negations; expressed in propositional logic as: ¬ (𝑝 ∧ 𝑞) ⇔ (¬ 𝑝) ∨ (¬ 𝑞).

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)

Forms of De Morgan's law

pluralDe Morgan's laws
alternative formDM

Origin of De Morgan's law

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

Questions about De Morgan's law

What does De Morgan's law mean?
De Morgan's law means the negation of a conjunction is the disjunction of the negations; expressed in propositional logic as: ¬ (𝑝 ∧ 𝑞) ⇔ (¬ 𝑝) ∨ (¬ 𝑞).
What part of speech is De Morgan's law?
De Morgan's law is a noun.
How do you pronounce De Morgan's law?
De Morgan's law is pronounced /dɨˈmɔɹɡɪnzˌlɔ/ (US).
What is the plural of De Morgan's law?
The plural of De Morgan's law is De Morgan's laws.

Words near De Morgan's law in the dictionary

  1. de Moivre's formula
  2. de Moivre's identity
  3. de Moivre's theorem
  4. De Morgan algebra
  5. De Morgan algebras
  6. De Morgan's law
  7. De Morgan's laws
  8. De Morgan's theorem
  9. De Munck
  10. de nada
  11. de novo

Source and license

Adapted from Wiktionary: De Morgan's law (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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