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Transitive relation

In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c.

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Field
Elementary algebra
Statement
A relation R {\displaystyle R} on a set X {\displaystyle X} is transitive if, for all elements a {\displaystyle a} , b {\displaystyle b} , c {\displaystyle c} in X {\displaystyl…
Symbolic statement
∀ a , b , c ∈ X : ( a R b ∧ b R c ) ⇒ a R c {\displaystyle \forall a,b,c\in X:(aRb\wedge bRc)\Rightarrow aRc}
Type
Binary relation

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Overview

Definition

Examples

Properties

Relation types that require transitivity

Counting transitive relations

Related properties

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Map overview Semantic statistics

Transitive relation

Nodes58
Edges57
Triples46
Avg. degree1.97
Density0.034483
Components1

How this topic connects Entity context

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Transitive relation

Top relations

related to Counting transitive relations · 13
Transitive relation → A000110, A006905, Brinkmann, However, Kleitman, Mala, McKay, No, OEIS, Pfeiffer, Rothschild, See, Since
related to Examples · 10
Transitive relation → Alice, Amy, As, Becky, Brenda, Carrie, Claire, For, In, On
related to Closure properties · 7
Transitive relation → For, Franklin, Franklin Pierce, Herbert Hoover, Hoover, Roosevelt, The
related to Transitive extensions and transitive closure · 6
Transitive relation → For, If, Let, R1, The, This
related to Other properties · 2
Transitive relation → For, When
Field · 1
Transitive relation → Elementary algebra
Statement · 1
Transitive relation → A relation R {\displaystyle R} on a set X {\displaystyle X} is transitive if, for all elements a {\displaystyle a} , b {\displaystyle b} , c {\displaystyle c} in X {\displaystyl…
Symbolic statement · 1
Transitive relation → ∀ a , b , c ∈ X : ( a R b ∧ b R c ) ⇒ a R c {\displaystyle \forall a,b,c\in X:(aRb\wedge bRc)\Rightarrow aRc}
Type · 1
Transitive relation → Binary relation
is a · 1
Transitive relation → preorder

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Important terminology

transitive relation set relations also example mathematics number displaystyle transitivity elements antitransitive reflexive binary preorder intransitive isbn one need r1

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Transitive relationFieldElementary algebra1.00infobox
Transitive relationStatementA relation R {\displaystyle R} on a set X {\displaystyle X} is transitive if, for all elements a {\displaystyle a} , b {\displaystyle b} , c {\displaystyle c} in X {\displaystyl…1.00infobox
Transitive relationSymbolic statement∀ a , b , c ∈ X : ( a R b ∧ b R c ) ⇒ a R c {\displaystyle \forall a,b,c\in X:(aRb\wedge bRc)\Rightarrow aRc}1.00infobox
Transitive relationTypeBinary relation1.00infobox
Transitive relationis apreorder0.90text
political questions or group preferences.Generalized to stochastic versionsinstance ofUnexpected examples of intransitivity arise in situations0.80text
Transitive relationrelated to Closure propertiesThe0.60section
Transitive relationrelated to Closure propertiesFor0.60section
Transitive relationrelated to Closure propertiesHerbert Hoover0.60section
Transitive relationrelated to Closure propertiesFranklin0.60section
Transitive relationrelated to Closure propertiesRoosevelt0.60section
Transitive relationrelated to Closure propertiesFranklin Pierce0.60section

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