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Disjunctive syllogism

In classical logic, disjunctive syllogism (historically known as modus tollendo ponens (MTP), Latin for "mode that affirms by denying") is a valid argument form which is a syllogism having a disjunctive statement for one of its premises.

Propositional logic, Related argument forms & Formal notation

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Field
Propositional calculus
Statement
If P {\displaystyle P} is true or Q {\displaystyle Q} is true, and P {\displaystyle P} is false, then Q {\displaystyle Q} is true.
Symbolic statement
P ∨ Q , ¬ P ∴ Q {\displaystyle {\frac {P\lor Q,\neg P}{\therefore Q}}}
Type
Rule of inference

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Overview

Propositional logic

Formal notation

Strong form

Related argument forms

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Disjunctive syllogism

Nodes37
Edges36
Triples13
Avg. degree1.95
Density0.054054
Components1

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Disjunctive syllogism

Top relations

related to Propositional logic · 6
Disjunctive syllogism → Equivalently, For, If, In, It, The
related to Related argument forms · 2
Disjunctive syllogism → Other, Unlike
Field · 1
Disjunctive syllogism → Propositional calculus
Statement · 1
Disjunctive syllogism → If P {\displaystyle P} is true or Q {\displaystyle Q} is true, and P {\displaystyle P} is false, then Q {\displaystyle Q} is true.
Symbolic statement · 1
Disjunctive syllogism → P ∨ Q , ¬ P ∴ Q {\displaystyle {\frac {P\lor Q,\neg P}{\therefore Q}}}
Type · 1
Disjunctive syllogism → Rule of inference
related to Formal notation · 1
Disjunctive syllogism → For

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Important terminology

syllogism disjunctive logic rule propositional displaystyle statement choose therefore disjunction argument example logical known one soup salad related also form

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Disjunctive syllogismFieldPropositional calculus1.00infobox
Disjunctive syllogismStatementIf P {\displaystyle P} is true or Q {\displaystyle Q} is true, and P {\displaystyle P} is false, then Q {\displaystyle Q} is true.1.00infobox
Disjunctive syllogismSymbolic statementP ∨ Q , ¬ P ∴ Q {\displaystyle {\frac {P\lor Q,\neg P}{\therefore Q}}}1.00infobox
Disjunctive syllogismTypeRule of inference1.00infobox
Disjunctive syllogismrelated to Formal notationFor0.60section
Disjunctive syllogismrelated to Propositional logicIn0.60section
Disjunctive syllogismrelated to Propositional logicIf0.60section
Disjunctive syllogismrelated to Propositional logicEquivalently0.60section
Disjunctive syllogismrelated to Propositional logicThe0.60section
Disjunctive syllogismrelated to Propositional logicFor0.60section
Disjunctive syllogismrelated to Propositional logicIt0.60section
Disjunctive syllogismrelated to Related argument formsUnlike0.60section

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