can you explain this in detailed steps

(b) Let Xn = (p, = 2, p2 = 3,pa =5,...,pn] be the set of the first n prime numbers. For example, Xs = {2, 3,5,7, 11). Let S,") = {a EN: v0 sign, 30 r, S me N,p; EX,.a = p," . p2"2 . ... . p;"( . ... . Pn"n } be the set of integers that can be factorised into the multiplication of the first n prime numbers, where the multiplicity of each prime number is less than or equal to a positive integer m. (i) Given an example of the integer a e S; and explain why it is valid. [4 marks] (ii) Specify the cardinality of S,". Show your work. [4 marks] (iii) Let P(X,,) denote the power set of X,. Define the function f: S,m) - P(X, ) such that f(a) = {p: EX,: v0 sisn,r; > 0,a = p," . p2"2 . .... pn"hes,"). Show that f is surjective (i.e., onto) but not injective (i.e., not one-to-one). [9 marks]