Let S be a non-empty set and F a field. Let F^S be a vector space of all functions from S to F. Fix an element s0 in S. Prove that the subset W = {f ∈ F^S | f(s0) = 0} is a subspace of F^S.

A) W is closed under vector addition.
B) W is closed under scalar multiplication.
C) W contains the zero vector.
D) All of the above.