Transitive relation

In mathematics, a 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 $c$ . Each partial order as well as each equivalence relation needs to be transitive.

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Transitive relation
Type	Binary relation
Field	Elementary algebra
Statement	A 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 $c$ .
Symbolic statement	$\forall a,b,c\in X:(aRb\wedge bRc)\Rightarrow aRc$

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