Further,
(a, b) ∈ R1 ∩ R2 ⇒ (a, b) ∈ R1 and (a, b) ∈ R2 ⇒ (b, a) ∈ R1 and (b, a) ∈ R2 ⇒
(b, a) ∈ R1 ∩ R2, hence, R1 ∩ R2 is symmetric Similarly, (a, b) ∈ R1 ∩ R2 and
(b, c) ∈ R1 ∩ R2 ⇒ (a, c) ∈ R1 and (a, c) ∈ R2 ⇒ (a, c) ∈ R1 ∩ R2 This shows that
R1 ∩ R2 is transitive Thus, R1 ∩ R2 is an equivalence relation