Which of the following are subspaces of F[0, 1]? Support your answer.
(a) U = {f | f(0) = 0}
(b) U = {f | f(x) ≥ 0 for all x in [0, 1]}
(c) U = {f | f(x + y) = f(x) + f(y) for all x and y in [0, 1]}