Let G be a group (written additively), Sa nonempty set, and M(S,G) the set of all functions ∫: S → G. Define addition in M(S,G) as follows: (∫ + g) : S → G is given by sI→ ∫(s) + g(s) ϵ G. Prove that M(S,G) is a group, which is abelian if G is.