If U and Ware subspaces of V, define their intersection U W as follows: U

Question:

If U and Ware subspaces of V, define their intersection U ∩ W as follows:
U ∩ W = {v|v is in both U and W}
(a) Show that U ∩ W is a subspace contained in L and W.
(b) Show that U ∩ W {0} if and only if {u, w} is independent for any nonzero vectors u in U and w in IV.
(c) If B and D are bases of U and W, and if U ∩ W = {0}, show that B ∪ D = {v | v is in B or D} is independent.