I've been brushing up on some Linear Algebra, and came across this puzzler in a proof book. I'm stuck, and looking for someone who has a proof for this. Here's the statement:

Let V be a vector space of dimension n, with a basis B = {u(1),...,u(n)}.

Let W be a subspace of V with dimension k with 1 <= k <= n.

There exists a subset of B which is a base for W. Prove this is true, or provide a counterexample.

Any help on this would be appreciated!