# Transitive Relation > [!Example] Transitive Relation > A *transitive* [[relation]] is a binary relation $R$ on a [[set]] $X$ such that for every $x, y, z\in X$, if $xRy$ and $yRz$, then $xRz$. > > That is, $(x,y)$, $(y,z)$, and $(x,z)\in R$. > $\forall\;x,y,z\in X:(xRy\wedge yRz)\implies xRz$ > > > [!Visual definitions]+ > > In a directed graph, a relation is transitive if and only if a pair of vertices connected by a *path of arrows* also has a *single arrow connecting the endpoints*. > > > > ![[TransitiveRelationGraph.svg]]