Not exactly sure how to approach the problem, since they are direct sums I know W1 intersect W2 {0} but their bases have an intersection that's the empty set. I know that the vectors included in each of the bases are linearly independent and have no redundant vectors therefore I think it's safe to assume that the bases themselves have no elements of any other base.

4. Let V = WOW, be a direct sum of finite-dimensional subspaces WI, W2 satisfying dim W1 = n, dim W2 = m. Let B1 = {b1, ...bn}, B2 = {c1, .... Cm} be bases of WI, W2 respectively. (a) Carefully show that BinB2 = 0 (b) Show B = B, UB, is a basis for V (c) Conclude that dim V = dim W, + dim W2