# Math Help - Help proving a subset is a subspace

1. ## Help proving a subset is a subspace

"Let V be a vector space, and let W1 and W2 be subspaces of V. Prove that (W1 ^ W2) is a subspace of V."

by ^ I mean the intersection of W1 and W2.

I'm not sure how to do this... (W1 ^ W2) is obviously a subset of V but how do you prove it has closure under vector addition and scalar multiplication?

$u,v\in W_1 \cap W_2$
$\Rightarrow u,v\in W_1 \land u,v\in W_2$
$\Rightarrow u+v\in W_1 \land u+v\in W_2$
$\Rightarrow u+v\in W_1 \cap W_2$