Sw that ltxgtch for every subgroup h such that xch thus

Question

If X is a nonempty subset of a group G,

let ={x1^(k1),x2^(k2)...xm^(km)|m>=1, xiEX and kiEZ for each i}.

a) show that is a subgroup of G that contains x.

b) show that C=H for every subgroup H such that XC=H. Thus is the smallest subgroup of G that contains X, and is called the subgroup generated by X.

note: E denotes element of, and C= denotes set containment