Question

If R and R′ are symmetric relation (not disjoint) on a set A, then the relation R ∩ R′ is

(1) reflexive

(2) symmetric

(3) transitive

(4) none of these

Answer 1

Correct option (2) symmetric

Explanation: 

(x, y) ∈ R ∩ R′

⇒ (x, y) ∈ R and (x, y) ∈ R′

⇒ (y, x) ∈ R and (y, x) ∈ R′

since R and R′ are symmetric. 

⇒ (y, x) ∈ R ∩ R′

⇒ R ∩ R′ is symmetric.