# Math Help - Span problem

1. ## Span problem

How do I prove the following:

Show that if S1 and S2 are arbitrary subsets of a vector space V, then span (S2 U S2) = span(S1) + span(S2).

2. Originally Posted by very_unique
How do I prove the following:

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 $v\in \text{spam}(S_1\cup S_2)$ then $v\in \text{spam}(S_1)+\text{spam}(S_2)$ and vice-versa.