Thread: Normal subgroups of a group

I have two normal subgroups (call them and ) of a group with only the identity element in common and need to show that for all .

I really have no idea where to begin although I do understand the definition of a normal subgroup. I think that is in but am not sure what this means, whether or not is a normal subgroup or whether I am meant to look for a homomorphism or isomorphism.

Any help appreciated, thanks.

Notice that the element is in both X and Y (why?) and must therefore be the identity element.