# 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.

Type Binary relation Elementary algebra A relation ${\displaystyle R}$ on a set ${\displaystyle X}$ is transitive if, for all elements ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c}$ in ${\displaystyle X}$, whenever ${\displaystyle R}$ relates ${\displaystyle a}$ to ${\displaystyle b}$ and ${\displaystyle b}$ to ${\displaystyle c}$, then ${\displaystyle R}$ also relates ${\displaystyle a}$ to ${\displaystyle c}$. ${\displaystyle \forall a,b,c\in X:(aRb\wedge bRc)\Rightarrow aRc}$