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

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