P union Q will equal the set of all vectors coming from either P or Q.

P + Q will equal the set of all vectors that look like p + q, where p in P and q in Q.

Sp ( P union Q ) will equal the set of all linear combinations of vectors coming from P union Q.

1 and 2 are not necessarily the same, I wouldn't think: the zero vector of one space need not be the zero vector of another space, although the zero vector of any given space is unique.

That's all I have time for right now.