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

Let be a set. Let be a relation between and . is reflexive if for all in . is symmetric if for all and in , and but and are not the same element. is transitive if for any and in , and implies . An example of an equivalence relation is congruence relation.

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