Chapter 3, Problem 41E

Let Sbe a subset of a group and let H be the intersection of all subgroups of G that contain S.
a. Prove that $\langle S\rangle =H$ .
b. If S is nonempty, prove that $\langle S\rangle =\{s_1^{n}1s_2^{n}2\dots s_m^{n}m|m\ge 1,s_i\in S,n_i\in Z\}$ . (The siterms need not be distinct.)