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Contraposition

In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent negated and swapped.

Traditional logic, Proofs & Proof by contrapositive

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Overview

Intuitive explanation

Formal definition

Proofs

Comparisons

Traditional logic

Distinguished from transposition

Proof by contrapositive

In nonclassical logics

In probability theory

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Map overview Semantic statistics

Contraposition

Nodes96
Edges95
Triples54
Avg. degree1.98
Density0.020833
Components1

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Contraposition

Top relations

related to In probability theory · 10
Contraposition → Assume, Bayes, FALSE, Hence, In, It, Pr, The, This, TRUE
related to Proof by contrapositive · 9
Contraposition → Because, By, However, If, One, The, Therefore, This, To
related to Distinguished from transposition · 7
Contraposition → All, In, No, Since, The, This, While
is a · 6
Contraposition → form of immediate inference in which a proposition is inferred from another and where the former has for its subject the contradictory of the original logical proposition's pred…, method of inference which may require the use of other rules of inference, schema composed of several steps of inference involving categorical propositions and classes, simultaneous interchange and negation of the subject and predicate, type of immediate inference in which from a given categorical proposition another categorical proposition is inferred which has as its subject the contradictory of the original…, valid form of immediate inference only when applied to
related to Subjective logic · 6
Contraposition → Bayes, FALSE, Hence, In, The, TRUE
related to External links · 4
Contraposition → Fallacy Files, Media, Wikimedia CommonsImproper Transposition, Wiktionary-logo-en-v2
related to Example · 3
Contraposition → Although, Let, The
related to Traditional logic · 3
Contraposition → For, If, In

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Important terminology

statement true displaystyle contrapositive proposition logic conditional one false inference propositions transposition also original proof theorem predicate inferred equivalent rule

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Contrapositionis aform of immediate inference in which a proposition is inferred from another and where the former has for its subject the contradictory of the original logical proposition's pred…0.90text
Contrapositionis aschema composed of several steps of inference involving categorical propositions and classes0.90text
Contrapositionis asimultaneous interchange and negation of the subject and predicate0.90text
Contrapositionis avalid form of immediate inference only when applied to0.90text
Contrapositionis amethod of inference which may require the use of other rules of inference0.90text
Contrapositionis atype of immediate inference in which from a given categorical proposition another categorical proposition is inferred which has as its subject the contradictory of the original…0.90text
thisinstance ofIn a conditional0.80text
Pinstance ofIn a conditional0.80text
proof by contradiction can also be used with contrapositioninstance ofindirect methods0.80text
asinstance ofindirect methods0.80text
for exampleinstance ofindirect methods0.80text
in the proof of the irrationality of the square root of 2instance ofindirect methods0.80text

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