We are given:
1. h: G -> G' is a group homomorphism.
2. M is a normal subgroup of G'.
3. N is the set of x in G such that h(x) is in M.
Prove that N is a normal subgroup of G.
It's not that hard for me to prove that N is a subgroup of G--that just comes from the fact that h is a group homomorphism. But I really have no idea how to prove that N is not just a subgroup but a normal subgroup. In fact, these normal subgroup proofs are just plain difficult for me right now. Please help.