Q2 (a) Let U = {-5,5,7) and H: P(U)→→P(U) be the function defined by H(X)=XnN.

Determine the image of H.

(b) Consider the function g: P ({0,2,3}) → {0,2,3} defined by g(X) = |X|.

Prove that g is surjective.

(c) Let F: R² → R³ and G: R³ → R² be given by

F(x, y) = (x, y,2y).

G(x, y, z) = (x, y+z/3).

(i) Determine the compositions F. G and G. F.

(ii) Is G the inverse of F? Justify your answer.

(iii) Show that G is not injective.