Question 2 Only parts a), b) and c) will be marked. Let V be a vector space and let S₁ and S₂ be non-empty subsets of V. (a) Show that if

S₁ S₂, then Span(S₁) Span(S₂). (b) Show that if S₁ S2, S1 S₂ and Span(S₁) = Span (S₂), then S₂ is linearly dependent. (c) Show that if S₁ and S₂ are linearly independent, then S₁ S₂ is linearly independent. (d) Give a counterexample to show that the following statement is false: "if S₁ and S₂ are linearly dependent, then S₁ S₂ is linearly dependent."