Let R be the relation in the set A = {a, b, c, d} given by R = {(a, a), (b, b) (c, c), (a, b), (b, a), (c, d), (d, d), (d, c)}

R is an equivalence relation

A = {a, b, c, d}

A = {a, b, c, d} given by R = {(a, a), (b, b) (c, c), (a, b), (b, a), (c, d), (d, d), (d, c)}

i) ∵ (a, a) ∈ R ∀ a ∈ A

ii) If (x, y) ∈ R ⇒ (y, x) ∈ R ∴ R is symmetric.

iii) R is transitive also.

∴ R is an equivalence relation.

So, option D is correct.