Here is the example:

The mapping from S_n to Z_2 that takes an even permutation to 0 and an odd permutation to 1 is a homomorphism.

-I have to prove that this example is a homomorphism.

I have looked at other homomorphisms and I understand how to prove them. They are pretty easy, such as determinants or derivatives. For some reason this one just eludes me, and I feel that there is a simple answer. i know that i have to prove phi(ab)=phi(a)phi(b) . this is an additive group so i think it would be phi(a+b)=phi(a)+phi(b) right? and i maybe have to do two cases one for even, one for odd? Thanks for help in advance.