De Morgan's laws

E428884

Boolean algebra law logical law rule of inference set theory law

De Morgan's laws are fundamental rules in Boolean algebra and set theory that relate conjunctions and disjunctions through negation, forming a cornerstone of classical logic.

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All labels observed (3)

Label	Occurrences
De Morgan's laws canonical	2
De Morgan's laws for propositions	1
De Morgan's laws for sets	1

How this entity was disambiguated

This entity first appeared as the object of triple T4290508 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: De Morgan's laws
Context triple: [Augustus De Morgan, knownFor, De Morgan's laws]

A. Herbrand disjunction
Herbrand disjunction is a logical formula formed as a finite disjunction of ground instances of a first-order formula, central to Herbrand’s theorem in proof theory and automated reasoning.
B. An Investigation of the Laws of Thought
An Investigation of the Laws of Thought is George Boole’s foundational 1854 treatise that established Boolean algebra and helped lay the groundwork for modern mathematical logic and computer science.
C. Leibnizian logic
Leibnizian logic is the rationalist, formal approach to logic and calculation developed by Gottfried Wilhelm Leibniz, emphasizing symbolic representation, logical calculus, and the reduction of mathematical and philosophical reasoning to precise logical principles.
D. Kirchhoff's circuit laws
Kirchhoff's circuit laws are fundamental rules in electrical engineering that describe how electric charge and energy are conserved in electrical circuits through relationships among currents and voltages.
E. Kluge's law
Kluge's law is a proposed sound law in Proto-Germanic historical linguistics that explains the development of certain geminate consonants from earlier consonant clusters.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: De Morgan's laws
Target entity description: De Morgan's laws are fundamental rules in Boolean algebra and set theory that relate conjunctions and disjunctions through negation, forming a cornerstone of classical logic.

A. Herbrand disjunction
Herbrand disjunction is a logical formula formed as a finite disjunction of ground instances of a first-order formula, central to Herbrand’s theorem in proof theory and automated reasoning.
B. An Investigation of the Laws of Thought
An Investigation of the Laws of Thought is George Boole’s foundational 1854 treatise that established Boolean algebra and helped lay the groundwork for modern mathematical logic and computer science.
C. Leibnizian logic
Leibnizian logic is the rationalist, formal approach to logic and calculation developed by Gottfried Wilhelm Leibniz, emphasizing symbolic representation, logical calculus, and the reduction of mathematical and philosophical reasoning to precise logical principles.
D. Kirchhoff's circuit laws
Kirchhoff's circuit laws are fundamental rules in electrical engineering that describe how electric charge and energy are conserved in electrical circuits through relationships among currents and voltages.
E. Kluge's law
Kluge's law is a proposed sound law in Proto-Germanic historical linguistics that explains the development of certain geminate consonants from earlier consonant clusters.
F. None of above. chosen

Statements (48)

Predicate	Object
instanceOf	Boolean algebra law ⓘ logical law ⓘ rule of inference ⓘ set theory law ⓘ
appliesTo	logical connectives ⓘ set operations ⓘ
category	identity in Boolean algebra ⓘ theorem in logic ⓘ theorem in set theory ⓘ
componentOf	axioms of Boolean algebra ⓘ equational theory of Boolean algebras ⓘ
expresses	equivalence between negated conjunction and disjunction of negations ⓘ equivalence between negated disjunction and conjunction of negations ⓘ
field	Boolean algebra ⓘ classical logic ⓘ digital logic ⓘ propositional logic ⓘ set theory ⓘ
generalizationOf	De Morgan's laws for propositions ⓘ linked to: De Morgan's laws De Morgan's laws for sets ⓘ linked to: De Morgan's laws
hasConsequence	negation distributes over conjunction and disjunction in classical logic ⓘ
hasForm	¬(P ∧ Q) ≡ (¬P) ∨ (¬Q) ⓘ ¬(P ∨ Q) ≡ (¬P) ∧ (¬Q) ⓘ
hasSetForm	(A ∩ B)^c = A^c ∪ B^c ⓘ (A ∪ B)^c = A^c ∩ B^c ⓘ
historicalPeriod	19th century ⓘ
holdsIn	Boolean algebras ⓘ linked to: Boolean algebra classical propositional logic ⓘ set algebras ⓘ
namedAfter	Augustus De Morgan ⓘ
relatedTo	complementation laws in Boolean algebra ⓘ distributive laws ⓘ law of double negation ⓘ
relatesConcept	complement ⓘ conjunction ⓘ disjunction ⓘ intersection ⓘ negation ⓘ union ⓘ
usedIn	complementation of logical conditions in programming ⓘ conversion between CNF and DNF ⓘ derivation of normal forms ⓘ design of digital circuits ⓘ proof transformations ⓘ simplification of Boolean expressions ⓘ simplification of logical expressions ⓘ
validIn	finite Boolean algebras ⓘ infinite Boolean algebras ⓘ

How these facts were elicited

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Augustus De Morgan → knownFor → De Morgan's laws ⓘ

Augustus De Morgan → hasConceptNamedAfter → De Morgan's laws ⓘ

De Morgan's laws → generalizationOf → De Morgan's laws for sets ⓘ

linked to: De Morgan's laws

De Morgan's laws → generalizationOf → De Morgan's laws for propositions ⓘ