Let V be a vector space over a field F, and let be subsets of V.

a) Show that span(S) is a subspace of V.

b) Show that span(S) is a subset of Span(S').

c) Take and give an example to show that it is possible that Span(S) = Span (S') even though and .

d) Let U,W be subspaces of V. Prove that U+W is also a subspace of V.