1. The problem statement, all variables and given/known data Let U1; U2 be subspaces of the vector space V . Prove that their intersection U1 \ U2 is also a subspace of V 2. Relevant equations I see how any equations could be used here 3. 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.