Can someone give me hints on how to solve this problem?

This is from Pugh's Real Mathematical Analysis

Problem 89.

Recall that p is a cluster point of S if each M_r_p contains infinitely many points of S. The set of cluster points of S is denoted as S'

Prove:

a) If S is a subset of T then S' is a subset of T'

b) (The union of S and T)'=Union of S' and T'

c) S' = (cl(S))'

d) S' is closed in M; that is, S" is a subset of S' where S"=(S')'

e) Calculate N', Q', R', (R\Q)', Q"

f) Let T be the set of points {1/n:n in N}. Calculate T' and T"

g) Give an example showing that S" can be a proper subset of S'