(the second isomorphism theorem). let u and w be subspaces of a vector space v.
(a) show that the map t: w → (u+w)/u defined by
t(w) =w+u
is surjective. (you do not need to check that it is linear, though it evidently is.)
(b) by applying the first isomorphism theorem to t, conclude that
w/(un w) ≅ (u+w)/u.