I have to show this map is well-defined, here's what I did:
Let x , and let . Then .
You need to give us more information. For a quotient map of the form to be well-defined, it is necessary that should be constant on the cosets of . You haven't said anything about the nature of or , and you haven't actually proved anything.
You need to give us more information. For a quotient map of the form to be well-defined, it is necessary that should be constant on the cosets of . You haven't said anything about the nature of or , and you haven't actually proved anything.
I am given that C is a normal subgroup of A and D is a normal subgroup of B. What else is needed to show is well-defined?
In that case, there isn't much to prove. You want to show that depends only on the cosets aC and bD, and that is immediately obvious from the way that is defined.