The correct option is D an equivalence relation
(a, b) R (a, b) because a + b = b + a. So, r is reflexive.
(a, b)R (c, d) ⇒ a+d = b+c ⇒ c+b = d+a
⇒ (c,d) R (a,b)
So, R is symmetric.
(a, b) R (c, d) and (c, d) R (e, f)
⇒ a + d = b + c, c + f = d + e
Adding, a + d + c + f = b + c + d +e
⇒ a + f = b + e
⇒ (a, b) R (e, f).
∴ R is transitive.