Algebra - Isomorphism Theorems

Let h : G to H be a surjective homomorphism of groups. If N is a normal subgroup of H, show that G/h^{-1}(N) is isomorphic to H/N. Let G be a group. Let H, K and L be three subgroups of G, such that H is a normal subgroup of K and H is a normal subgroup of L. Show that the subgroup M of G generated by K and L is contained in the normalizer N_G(H) = {g in G : g H g^{-1} = H} of H in G. Let K be a field. Use the second isomorphism theorem to show that B(2, K) / U(2, K) is isomorphic to T(2, K), where B(2, K) is the set of 2 x 2 upper triangular matrices with nonzero determinant, U(2, K) is the set of 2 x 2 upper triangular matrices with 1_K in diagonal entries, T(2, K) is the set of 2 x 2 diagonal matrices with nonzero determinant.