De Morgan's law
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De Morgan's law
- /dɨˈmɔɹɡɪnzˌlɔ/ US
Where it comes from
Named after the British mathematician and logician Augustus De Morgan (1806–1871), who first formulated the laws in formal propositional logic.
noun De Morgan's laws · DM
- 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 argume
- The negation of a disjunction is the conjunction of the negations; expressed in propositional logic as: ¬ (𝑝 ∨ 𝑞) ⇔ (¬ 𝑝) ∧ (¬ 𝑞)
- The complement of a union is the intersection of the complements; as expressed by: (𝐴 ∪ 𝐵)′ = 𝐴′ ∩ 𝐵′
- The complement of an intersection is the union of the complements; as expressed by: (𝐴 ∩ 𝐵)′ = 𝐴′ ∪ 𝐵′
- Any of various laws similar to De Morgan’s laws for set theory and logic; for example: ¬∀𝑥 𝑃(𝑥) ⇔ ∃𝑥 ¬𝑃(𝑥)
Translations
Every language
noun law of formal logic
| Deutsch | De Morgen'sches Gesetz |
|---|
noun law of set theory
| Deutsch | De Morgen'sches Gesetz |
|---|
Talk about this word "De Morgan's law." Wiktionary, via Micwyn, micwyn.com/word/de%20morgan's%20law. Accessed 6 Nov. 2026. De Morgan's law. (n.d.). In Wiktionary, via Micwyn. Retrieved November 6, 2026, from https://micwyn.com/word/de%20morgan's%20law "De Morgan's law." Wiktionary, via Micwyn. Accessed November 6, 2026. https://micwyn.com/word/de%20morgan's%20law.Cite this
@misc{de_morgan_s_law_2026,
title = {De Morgan's law},
howpublished = {Wiktionary, via Micwyn},
year = {2026},
url = {https://micwyn.com/word/de%20morgan's%20law},
urldate = {2026-11-06}
}
