Let V and W be a vector space, and let S be a subset V. Define S^0 = { T \in L(V,W): T(x)= 0 \ \forall x \in S}. (Where L(V,W) denotes a linear transformation from V \rightarrow W). Prove the following statements:

a) S^0 is a subspace of L(V,W)
b) S_1 and S_2 are subsets of V and S_1 \subset S_2, then S^{0}_{2} \subset S^{0}_{1}.

I have no idea how to even approach this problem, any help would be appreciated.

Thanks in advance.