Let $V$ be a vector space. Let $S$ and $T$ be subsets (not necessarily subspaces) of $V$.

Question

Is it necessarily true that:

(a) Span$(S+T)$ $\subseteq$ Span$(S)$ + Span$(T)$

(b) Span$(S+T)$ $\supseteq$ Span$(S)$ + Span$(T)$

The question also hints to use theorem 4.13 which states:

'Let $V$ be a vector space. Let $S$ be a subset of $V$ . Then Span$(S)$ is the intersection of all subspaces $U$ of $V$ such that $S \subseteq U$.'

Despite the hint/clue however, I still don't know how to even begin to tackle this question. Any guidance would be greatly appreciated.