Please answer it as soon as possible. Abstract Algebra.

8. (20 PTS) PROOFS! Do two of the following three proofs. Be sure to indicate which two you are doing. A. Let a and ,6 be group homomorphisms from G to E Prove that H ={ge G:a[g)=,3(g)] is a subgroup of G. B. Show that the only ring homomorphism : 2.50 > Z is the trivial homomorphism x} = D . C. Let A and B be ideals of the ring R with AHB ={0]. Prove that for any elements x6 A and ye B , we must have xy = 0