How do I prove that the zero vector in V is also the zero vector in W?

Let W be a subspace of the vector space V. Prove that the zero vector in V is also the zero vector in W.





I need a proof for this desperately. I got a mid-term tomorrow.|||Since W is contained in V then g+0=g in V for any g in W and 0 the zero vector in V. So 0 in V behaves like the zero vector in W. 0 is also contained in W since g-g = 0 as a relation in V, must also hold true in W. If h is another vector in W with the same properties as 0, then h+0=0, and from above h+0=h, so 0=h.