Please solve (d) and (f) parts

1. Use the axioms of ZFC to prove the following. (a) For each set x, there is a set S satisfying S = (x). (b) For any sets X, Y, there is a set S satisfying S = (Z : ZEXVZEY). We denote this set S by XUY and call it the union of X and Y. CAUTION: The Union axiom alone doesn't imply this. (c) For any sets x, y, there is a set S satisfying S = {{x), (x, y)). We denote this set S by (x, y) and call it the ordered pairing of x, y or just an ordered pair. (d) For any sets X, Y, there is a set S satisfying S= (z:xEXAyeYAZ= (x,y)). We denote this set by X x Y and call it the Cartesian product of X and Y. CAUTION: Comprehension only gives the existence of sets of the form (zEZ : xEXAyeYAZ= (x,y)) for a set Z, so to apply it, one has to first prove the existence of an appropriate Z. (e) [Optional, no credit] Show the existence of X x Y without using the Powerset axiom. (f) For any sets X, Y, write down a formula o(f) such that for any set f, p(f) holds if and only if f is a function from X to Y. Prove that there is a set S satisfying S = {f : p(f)). We denote this set S by YX and call it the set of all functions from X to Y