If H=K, or one is contained in another is trivial. Let h be in H but not in K and k be in K but not in H. Then imagine h*k is in H. then h*k=h' or equivalently k=h^-1*h', which is a contradition, because it would mean k is in H. Similarly for the supposition that h*k=k'. Thus h*k is not in H or K, but is in G. QED