Proving a set is a subspace

Hey everybody,

My tutor has found an old exam online and is having me complete it as a preparatory exercise before my final exam this week. I'm having trouble even wrapping my head around this one, so I'm hoping someone here can help me through it!

(note: the ^ symbol is supposed to be a perpendicular symbol)

Let W be a subspace of the inner product space V. Define

W^ = {v in V: <v,w> = 0 for all w in W}

(a) Prove that W^ is a subspace of V .

If you'd like the test itself, its found at this address, problem number 12.a:

http://www.math.niu.edu/courses/math...Fa04-final.pdf

Thanks so much for any help!