Suppose that H and K are subgroups of a group G. Prove the following statements under additional conditions:

(a). First, give an example that HK may not be a subgroup of G.

(b). Prove that if H is a normal subgroup of G, then HK is a subgroup of G.

(c). Prove that if both H and K are normal subgroups of G, then HK is a normal subgroup of G.