Let U1; U2 be subspaces of the vector space V . Prove that their intersection U1 \ U2 is
also a subspace of V
I see how any equations could be used here
The Attempt at a Solution
Well intuitively this seems obvious from the get go. If U1 and U2 are subspaces, then their intersection, which can at most contain all of U1 if U1=U2, and at the very least the 0 vector if U1 and U2 share no common vectors other than the 0 vector. But I don't know how to prove this. It seems like from what I've said, I've neglected all of the intermediate possibilities.