Let W1,W2 be subspaces of a vector space. (a) Assume that the set S1 spans W1, and

Question:

Let W1,W2 be subspaces of a vector space.
(a) Assume that the set S1 spans W1, and that the set S2 spans W2. Can S1 ∪ S2 span W1 +W2? Must it?
(b) Assume that S1 is a linearly independent subset of W1 and that S2 is a linearly independent subset of W2. Can S1 ⊂ S2 be a linearly independent subset of W1 +W2? Must it?