la. (6 pointsl Write out P(P(E2) without using P. (Recall PO means power set.) g P. (Recall P) means power 1b. [6 pointsl Write out P((0,1,(2)n P f1,2) without using P 1c. [6 points) Suppose S T are nonempty sets. For each of the following four propositions, say whether it's guaranteed to be true, guaranteed to be false, or possibly true / possibly false, and justify your answer. SE P(T) T P(S) E P(T) SS P(T) T P(S) S P(T) 1d. [6 points] Explain in English why the following is true: (10, 1,2)*x(a, b)") n({0, 1)"x(a, b, c)') (0,1 1x {a, b)' le. [6 points] Define Z4 [0, 1,2). Let the function f: Zs x Zs Zs be defined by f(,y)(+ y mod 3), and let g: Zs x ZsZs be defined by g(z, y) (y mod 3). Write out the 2-dimensional table representing the function h: (23 x Z3) x ZsZs defined by h((z, y),z) g(,f (,2))