Question

Let Si₁ and S₂ be subsets of a vector space V. Prove that span(S₁ ∩ S₂) C span(S₁) ∩ span(S₂). Give an example in which span(S₁ ∩ S₂) and span(S₁) ∩ span(S₂) are equal and one in which they are unequal.