Question

Does span(S1 intersect S2)=Span(S1) intersect Span(S2)?

Answer 1

yup:)

Answer 2

Can you explain why?

Answer 3

first
Prove that span(S1 ∩ S2) ⊆ span(S1) ∩ span(S2)
by definition of intersection both S1 and S2 contain S1∩S2
so span(S1 ∩ S2) ⊆ span(S1)
and span(S1 ∩ S2) ⊆ span(S2)
so they will be ⊆ of their intersection also
and reverse is similarly can be proved or other way is venn diagram
:)