Question

Let S and T be non-empty subsets of $\R^2$, and W be a non-zero proper subspace of $\R^2$. Consider the following statements :
I. If span(S) = $\R^2$ , then span(S ∩ W) = W.
II. span(S ∪ T) = span(S) ∪ span(T).
Then

• A. both I and II are TRUE
• B. I is TRUE but II is FALSE
• C. II is TRUE but I is FALSE
• D. both I and II are FALSE

Answer 1

Answer: (D)

both I and II are FALSE

Answer 2

The correct option is (D) : both I and II are FALSE.