1. The problem statement, all variables and given/known data Suppose that V is a vector space, W and X are subspaces with X contained in W. Show that there is a subspace U of V which is maximal subject to the property that U intersect W equals X. 2. Relevant equations N/A 3. The attempt at a solution I know this uses Zorn's Lemma but I can't see how to apply it. Thanks for any help in advance!