I need to prove that these statements are true or false.

1. It is possible to find a pair of two-dimensional subspaces S and T of R³ such that S ∩ T = {0}

2. If S and T are subspaces of a vector space V, then S U T is a subspace of V.

3. If S and T are subspace of a vector space V, then S ∩ T is a subspace of V.

I understand that the two closure identities need to be met in order to be a subspace. However the intersection and union properties are throwing me off. Can anyone help me with this? Thank you.