de morgan's law
/dɨˈmɔɹɡɪnzˌlɔ/
Word Rarity
Rare
Frequency: Zipf frequency 3.08 in modern English
19
Scrabble Score
12
Letters
3
Syllables
11
Unique Chars
Meaning
noun
Either of two laws in formal logic which state that:
noun
Either of two laws in formal logic which state that:
noun
Either of two laws in set theory which state that:
noun
Either of two laws in set theory which state that:
noun
Any of various laws similar to De Morgan’s laws for set theory and logic; for example: ¬∀𝑥 𝑃(𝑥) ⇔ ∃𝑥 ¬𝑃(𝑥)
Example Sentences
- "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 argument may be formalized as follows: (1) [(p & q) & r] → s Premiss (2) ~s Premiss (3) ~[(p & q) & r] 1, 2 MT (4) ~(p & q) v ~r 3 DM (5) r Premiss (6) ~(p & q) 4, 5 DS (7) ~p v ~q 6 DM (3) follows from the conjunction of (1) and (2) by modus tollens; De Morgan’s law applied to (3) yields (4); (4) and (5) together lead to (6) by disjunctive syllogism; and another application of De Morgan’s law takes us from (6) to the final conclusion, according to which either God exists or there is free will (but not both)."
Etymology
Named after the British mathematician and logician Augustus De Morgan (1806–1871), who first formulated the laws in formal propositional logic.
Regional Pronunciation
- American English: /dɨˈmɔɹɡɪnzˌlɔ/