Is the Intersection of Subspaces a Subspace?

[jeffreylze]

Homework Statement

Let H and K be subspaces of a vector space V. Prove that the intersection K$$\cap$$ H is a subspace of V.

Homework Equations

The Attempt at a Solution

This, I have absolutely NO idea how and where to start. Are there any axioms which can be used to prove this?

 

[NoMoreExams]

What does it mean to be a subspace of a vector space?