Mark each statement True or False. Justify each answer. (a) If f : A → B and C is a nonempty subset of A, then f (C ) is a nonempty subset of B. (b) If f : A → B is surjective and y ∈ B, then f – 1(...

Mark each statement True or False. Justify each answer.

(a) If f : A → B and C is a nonempty subset of A, then f (C ) is a nonempty subset of B.

(b) If f : A → B is surjective and y ∈ B, then f – 1( y) ∈ A.

(c) If f : A → B and D is a nonempty subset of B, then f – 1(D) is a nonempty subset of A.

(d) The composition of two surjective functions is always surjective.

(e) If f : A → B is bijective, then f – 1 : B → A is bijective.

(f ) The identity function maps
 onto {1}.