(a) Let P : S → S be the functor that assigns to each set X its power set (set of all subsets) P(X) and to each function ∫: A → B the map P(∫) : P(B) → P(A) that sends a subset X of B onto ∫^-1(X) ⊂ A. Then P is a representable contra variant functor.

(b) Let the object function of Q : S → S be defined by Q(A) = P(A). If ∫: A → B, let Q(∫): Q(A) → Q(B) be given by X|→ ∫(X). Then Q is a covariant functor. Is Q representable?