Relations and Functions

A relation R on a set A is an Equivalence Relation if it satisfies three properties:

1. Reflexive: (a, a) ∈ R for every a ∈ A.
2. Symmetric: If (a, b) ∈ R, then (b, a) ∈ R.
3. Transitive: If (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R. An equivalence relation divides a set into disjoint equivalence classes.