## Subspace, subset and linear transf. problem

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.