Given subspaces H and K of a vector space V, the sum of H and K, written

Question:

Given subspaces H and K of a vector space V, the sum of H and K, written as H + K, is the set of all vectors in V that can be written as the sum of two vectors, one in H and the other in K; that is, H + K = {w: w = u + v for some u in H and some v in K}
a. Show that H + K is a subspace of V.
b. Show that H is a subspace of H + K and K is a subspace of H + K?