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De Morgan's laws

In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician. The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation.

History, Formal notation & Generalising De Morgan duality

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Overview

Formal notation

History

Proof for Boolean algebra

Proof for set theory

Generalising De Morgan duality

Extension to predicate and modal logic

In intuitionistic logic

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De Morgan's laws

Nodes61
Edges60
Triples65
Avg. degree1.97
Density0.032787
Components1

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De Morgan's laws

Top relations

related to history · 18
De Morgan's laws → Aristotle, Augustus De Morgan, De Morgan, De Morgan's, Dialectica, For, Formal Logic, George Boole, Greek, Jean Buridan, Medieval, Nevertheless, Nonetheless, Ockham, Still, Summulae, The, William
related to External links · 14
De Morgan's laws → Duality, EMS Press, Encyclopedia, Eric, Internet Encyclopedia, Language, Logic, Mathematics, MathWorld, Morgan's, Morgan's Laws, Philosophy, PlanetMath, Weisstein
has application · 7
De Morgan's laws → AND, Boolean, De Morgan's, Expressions, In, Negating, OR
related to Text searching · 7
De Morgan's laws → AND, Boolean, Consider, De Morgan's, NOT, OR, The
related to Worked Example · 6
De Morgan's laws → De Morgan's, Here, It, Let's, The, Using De Morgan's
related to In computer engineering · 4
De Morgan's laws → Boolean, De Morgan's, In, Therefore
related to In intuitionistic logic · 3
De Morgan's laws → Morgan's, Specifically, Three
related to Engineering · 2
De Morgan's laws → De Morgan's, In
related to Substitution form · 2
De Morgan's laws → De Morgan's, This

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Important terminology

de laws morgan's displaystyle negation logic overline conjunction disjunction cap true must form cup one set boolean also false logical

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
this are especially useful when simplifying logical expressions in proofsinstance ofStep-by-step rewrites0.80text
problem solvinginstance ofStep-by-step rewrites0.80text
De Morgan's lawshas applicationDe Morgan's0.60section
De Morgan's lawshas applicationBoolean0.60section
De Morgan's lawshas applicationExpressions0.60section
De Morgan's lawshas applicationIn0.60section
De Morgan's lawshas applicationNegating0.60section
De Morgan's lawshas applicationAND0.60section
De Morgan's lawshas applicationOR0.60section
De Morgan's lawsrelated to EngineeringIn0.60section
De Morgan's lawsrelated to EngineeringDe Morgan's0.60section
De Morgan's lawsrelated to External linksDuality0.60section

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