Let V and W be vectors spaces, and let S be subset of V. Define S^0 = { T \in \L(v,w) : T(x) =0 for all x \in \ S.

Prove the following statements

a) S^0 is a subspace of L(v,w)

b)If S1 and S2 are subsets of V and S1 subset S2, then S^0_2 less than or equal S^0_1.