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Transitive relation: Examples, Related properties & Properties

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.

Language: English [EN]
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Transitive relation topic overview

The analysis highlights Examples, Related properties and Properties as prominent areas in the source structure around Transitive relation.

Related topics
50
Source areas
7
Connected nodes
57
Extracted relationships
46
Concept neighborhoods
23
Bridge connections
57

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Examples · 11 topics
Related properties · 11 topics
Properties · 9 topics
Overview · 7 topics
Relation types that require transitivity · 7 topics
Definition · 3 topics
Counting transitive relations · 2 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

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

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Definition

Examples

Properties

Relation types that require transitivity

Counting transitive relations

Related properties

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Transitive relation connects Entity context

The extracted context around Transitive relation shows recurring relationship patterns in the source. For example, Transitive relation → A000110, A006905, Brinkmann, However, Kleitman, Mala, McKay, No, OEIS, Pfeiffer, Rothschild, See, Since Another extracted example is Transitive relation → Alice, Amy, As, Becky, Brenda, Carrie, Claire, For, In, On. Use these groups to spot repeated connection types before inspecting the individual relationships.

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

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

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

Transitive relation relationships Subject–Predicate–Object triples

TTTA extracted 46 structured relationships around Transitive relation. Examples in this analysis include Transitive relation → Field → Elementary algebra and Transitive relation → 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…. The table shows each extracted connection, where it came from and its confidence.

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

Related concept clusters Concept neighborhoods

The concept neighborhoods around Transitive relation bring nearby vocabulary together. In this analysis, examples include Transitive, Set and Relations. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Transitive relation
    • Transitive
    • Set
    • Relations
    • Displaystyle
    • Antitransitive
    • Xry
    • Need
    • R1
    • Reflexive
    • Defined
    • Closure
    • Extension
  • transitive relation
    • Transitive
    • Set
    • Relations
    • Displaystyle
    • Antitransitive
    • Xry
    • Number
    • Need
    • R1
    • Reflexive
    • Birth
    • Defined
  • binary relation
    • Transitive
    • Relates
    • Whenever
    • Elements
    • Also
    • Set
    • Displaystyle
    • Related
    • Antitransitive
    • Xry
    • Closure
    • Examples
  • equivalence relation
    • Transitive
    • Reflexive
    • Number
    • Set
    • Displaystyle
    • Relations
    • Antitransitive
    • Xry
    • Called
    • Preorder
    • Birth
    • Defined
  • homogeneous relation
    • Transitive
    • Set
    • Displaystyle
    • Antitransitive
    • Xry
    • Number
    • Birth
    • Defined
    • Need
    • Relations
    • Called
    • Closure
  • empty relation
    • Transitive
    • Set
    • Displaystyle
    • Antitransitive
    • Xry
    • Number
    • Birth
    • Defined
    • Need
    • Relations
    • Called
    • Closure
  • quasitransitive relation
    • Transitive
    • Set
    • Displaystyle
    • Antitransitive
    • Xry
    • Number
    • Birth
    • Defined
    • Need
    • Relations
    • Called
    • Closure
  • relation types that require transitivity
    • Transitive
    • Isbn
    • Set
    • Displaystyle
    • Antitransitive
    • Xry
    • Whenever
    • Number
    • Sets
    • Birth
    • Defined
    • Need

Connections between topic areas Semantic bridges

For Transitive relation, one of the stronger structural bridges in this analysis connects Transitive relation with Examples. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Transitive relationExamples · splits 46 ⟂ 12
Transitive relationRelated properties · splits 46 ⟂ 12
Transitive relationProperties · splits 48 ⟂ 10
Transitive relationOverview · splits 50 ⟂ 8
Transitive relationRelation types that require transitivity · splits 50 ⟂ 8
Transitive relationDefinition · splits 54 ⟂ 4
Transitive relationCounting transitive relations · splits 55 ⟂ 3

Map overview Semantic statistics

Transitive relation

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

Source & methodology

TTTA analyzes the structure around Transitive relation to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Examples, Related properties & Properties, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Transitive relation · EN edition · Analysis: TopicsToTalkAbout

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