# Equivalence relation

Definition : let ~ be a relation: ~ is an equivalence relation if it is reflexive, symmetric and transitive.

Let $G$ be a set. Let $R$ be a relation between $a$ and $b$. $R$ is reflexive if $aRa$ for all $a$ in $G$. $R$ is symmetric if for all $a$ and $b$ in $G$, $aRb$ and $bRa$ but $a$ and $b$ are not the same element. $R$ is transitive if for any $a, b,$ and $c$ in $G$, $aRb$ and $bRc$ implies $aRc$. An example of an equivalence relation is congruence relation.

Also See : Binary Relation, Congruence Relation, Reflexive Property, Symmetric Property, Transitive Property