How can I prove this problem?

Let V be an n-dimensional vector space with inner product ( , ). Let U and W be subspaces of V. Then we can define a set X as X = {u + we Vu EU, WEW} Note that the definition of X is the same as the definition of U O W except that we have removed the requirement that Un W = {0}. (a) Prove that X is a subspace of V. (b) Prove the following: If Un W / {0}, then there are u1, u2 E U and w1, W2 E W such that ul * u2 and w1 + w2, but ul + w1 = 12 + W2. (Sidenote: This is the inverse of Corollary 9.5.2, with X replacing UO W.)