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

a) $\displaystyle S^0$ is a subspace of $\displaystyle L(V,W)$

b) $\displaystyle S_1$ and $\displaystyle S_2$ are subsets of $\displaystyle V$ and $\displaystyle S_1 \subset S_2$, then $\displaystyle S^{0}_{2} \subset S^{0}_{1}$.

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

Thanks in advance.