Hail Mathematicians,

It's me again.

I have a problem, here is the appropriate theorem:

Theorem:Let be a group with operation , and let be a subset of . Then is a subgroup of iff

(a) is nonempty

(b) if and , then , and

(c) if , then

i've used this theorem over and over in studying, but i have trouble proving (b) and (c) in the following problem

Problem:

Assume that is a group with operation and let

Prove that is a subgroup of G.

This is a homework problem, so only hints please.

Thanks, guys and gals

EDIT: Proving it is nonempty is trivial, so don't even bother...