Let U and W be subspaces of Rn. Define their intersection U W and their sum

Question:

Let U and W be subspaces of Rn. Define their intersection U ∩ W and their sum U + W as follows:
U ∩ W={X in Rn | X belongs to both U and W}.
U+ W= {X in Rn | X is a sum of a vector in U and a vector in W}.
(a) Show that U ∩ W is a subspace of Rn.
(b) Show that U + W is a subspace of Rn.