Alright so I'm having a hard time trying to understand vector spaces and subspaces, however mainly subspaces is giving me a hard time. Here are 2 questions that are giving me the most difficulty..

1) Is the set W = {f (x) Є P(F): f(x) = 0 or f(x) has degree n} a subspace of P(F) if n > (or equal) 1? Justify your answer.

2) Prove that a subset W of a vector space V is a subspace of V if and only if 0 Є W and ax + y Є W whenever a Є F and x,y Є W


Appreciate the help in advance!