Transitive Relation

Transitive Relation

## Definition / Concept

A relation $R$ on $A$ is transitive if two consecutive relations imply the corresponding third relation.

## Formula

$$aRb,\ bRc\Rightarrow aRc$$

$$(a,b)\in R,\ (b,c)\in R\Rightarrow(a,c)\in R$$

## Conditions / Special Cases

The elements $$a$$, $$b$$ and $$c$$ need not be distinct.

## Usage

- Used in identifying equivalence relations and partial order relations.