Question

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): If A and B are non-empty sets then (A \(\cup\) B) - A = A \(\cap\) B\(^{C}\) is true.
Reason (R): Venn diagrams help to prove the some set relations.
In the light of the above statements, choose the most appropriate answer from the options given below:

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

If you are unsure of the algebraic laws of set theory during an exam, quickly sketch a 2-circle Venn diagram.
Shade \((A \cup B) - A\) (which is only the B region) and \(A \cap B^C\) (which is only the A region).
You will immediately see they do not overlap, proving Assertion (A) is false!

Answer 1

The Correct Option is D