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 Therefore, R is
symmetric Further, (a, b) ∈ R and (b, c) ∈ R ⇒ f (a) = f (b) and f(b) = f (c) ⇒ f (a)
= f(c) ⇒ (a, c) ∈ R, which implies that R is transitive