Let S₁ and 52 be subsets of a vector space V. Prove the followings: (1) span(S₁) Cspan(S₂). (2) span (S₁ S₂) C span (S₁) span (S2). Give an example in which span(S1 S₂) and span (S₁) n span(S₂) are equal and one in which they are unequal. (3) span(S₁ US₂) = span(S₁) + span(S₂).

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