Show that if S1 and S2 are arbitrary subsets of a vector space V, then span(S1 U S2) = span(S1) + span(S2)(adsbygoogle = window.adsbygoogle || []).push({});

When attempting it i used the definition of a union as well as the definition of the sum of two sets and I also used the fact that the union of two sets is the sum of all the elements in set1 plus all elements in set2 minus the intersection of the set. By this method, the only way to prove the above statement is for the intersection of the sets to be equal to zero, and it seems pretty obvious to me that the intersection of any two sets in V does not necessarily have to equal 0. Unless the word "abitrary" implies that? So just wondering if anyone can help me with this.

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# Prove span(S1 U S2) = span(S1) + span(S2)

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