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
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
I. If span(S) = \(\R^2\) , then span(S ∩ W) = W.
II. span(S ∪ T) = span(S) ∪ span(T).
Then
Updated On: Oct 1, 2024
- both I and II are TRUE
- I is TRUE but II is FALSE
- II is TRUE but I is FALSE
- both I and II are FALSE
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The Correct Option is D
Solution and Explanation
The correct option is (D) : both I and II are FALSE.
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