Let H be a group. LetMbe a normal subgroup of H. LetKbe any subgroup ofH.LetMK={m°k: m is an element of M and k is an element if K}

a)Prove: MK is a subgroup of H.

b)Suppose that M intersects K={I}. Let k, k' are elements of K. Prove M°k=M°k' if and only if k= k'. conclude that |MK|=|M||K|