Equivalence Relation

A binary relation $\sim$ on a set $X$ is said to be an equivalence relation, if and only if it is reflexive, symmetric and transitive. That is, for all $a,b$ and $c$ in $X$:

• $a\sim a$ (reflexivity)
• $a\sim b⟺b\sim a$ (symmetry)
• $(a\sim b)\wedge (b\sim c)⟹a\sim c$ (transitivity)