Let c:G1--->G2 and d:G2--->G3 be group homomorphisms. Prove that dc:G1--->G3 is a homomorphism. Prove that ker(c) is a subset of ker(d).

Since c and d are homomorphisms, we know c(ab)=c(a)c(b) and d(ab)=d(a)d(b).

We want to show dc(ab)=dc(a)dc(b)

I get stuck at this point.