A relation R in a set A is called an equivalence relation if

1. R is reflexive i.e. (a, a) ∈ R for all a ∈ A

2. R is symmetric i.e. (a, b) ∈ R => (b, a) ∈ R for all (a, b) ∈ A

3. R is transitive i.e. (a, b), (b, c) ∈ R => (a, c) ∈ R for all (a, b, c) ∈ A

The equivalence relation is denoted by symbol ~

The set of all elements of S that are equivalent to each other is called an equivalence class.

The equivalence relation partitions the set S into mutually exclusive equivalent classes.