I am having difficulty with vector subspaces. It would be helpful if someone could give me an answer to at least one of these two questions.

1.

Prove that is a subspace of F^n, but is not

2.

Is the set W = { f(x) P(F): f(x)=0 or f(x) has a degreen} a subspace of P(F) if n ≥ 1? Justify your answer