Let S: N ---> P(N) be the function defined by S(n) = {kn I k belongs to N} and M: P(N) ---> N be the function defined by:

M(A) = 1 if A = Empty Set

M in (A) if A does not equal an Empty Set

(a) Is S injective? Is S surjective? prove your claims.

(b) Is M injective? Is M surjective? prove your claims.

(c) For n belongs to N, find (M o S)|(n).

(d) For A belongs to P(N), find (S o M)(A).