Define a relation R in X given by
R = {(a, b): f(a) = f(b)} Examine whether R is an equivalence relation or not Solution For every a ∈ X, (a, a) ∈ R, since f(a) = f (a), showing that R is reflexive Similarly, (a, b) ∈ R ⇒ f (a) = f (b) ⇒ f (b) = f (a) ⇒ (b, a) ∈ R