Equivalence Relation

algebra

Definition

Equivalent Relation

An equivalence relation is a binary relation that is reflexive, symmetric and transitive.

1. reflexive: $\forall a\in A:aRa$
2. symmetric: $\forall a,b\in A:aRb⟹bRa$
3. transitive: $\forall a,b,c\in A:(aRb\wedge bRc)⟹aRc$