Let V be a vector space with subspaces U and W. Define the s u m of

Question:

Let V be a vector space with subspaces U and W. Define the s u m of U a n d W to be
U + W = {u + w: u is in U, w is in W}
(a) If V = R3, U is the x-axis, and W is the y-axis, what is U + W?
(b) If U and W are subspaces o f a vector space V, prove that U + W is a subspace of V.