Show that if S1 and S2 are arbitrary subsets of a vector space V, then span (S2 U S2) = span(S1) + span(S2).
Show that each one is a subset of eachother. Thus, if $\displaystyle v\in \text{spam}(S_1\cup S_2)$ then $\displaystyle v\in \text{spam}(S_1)+\text{spam}(S_2)$ and vice-versa.