(8 Marks) (a) In the notes we proved that if 4 : G - H is a homomorphism and H is cyclic, then G must be as well. Show that the converse is false. That is, find groups G and H, where G is cyclic, but H is not and a homomorphism 4 : G -> H. (b) Finish the proof of 1.13 (3): Given groups G and H and a homomorphism 4 : G - H. Show that if L is normal in H, then 4 (L) is normal in G. (Note that we showed in the notes that 4 (L) is a subgroup, so you don't have to show that.)