Let us take an example:

Let R = {a, b, c}

and the relation A is defined as

A = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c)}

1. Reflexive:

Since, (a, a), (b, b), (c, c) ∈ A

So, A is reflexive on R

2. Symmetry:

Since, (a, b) ∈ A and (b, a) ∈ A

and (a, c) ∈ A and (c, a) ∈ A

So, A is symmetry on R

3. Transitive:

Since, (a, b), (b, c) ∈ A => (a, c) ∈ A

and (a, c), (c, a) ∈ A => (a, a) ∈ A

So, A is tranisitive on R

Hence, A is an equiavlence relation on R

Now, Domain (A) = {a, b, c}

and Range(A) = {a, b, c}

Now, Domain(A) = Range(A) = {a, b, c} = A

Hence, if A is an equivalence relation on R then Domain(A) = Range(A) = R