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
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...