Question

Assertion : For any two sets $A$ and $B,A-B\subset B^{\prime }$
Reason : If A be any set, then $A\cap A^{\prime }=\varphi$

• A. Assertion is correct, reason is correct; reason is a correct explanation for assertion.
• B. Assertion is correct, reason is correct; reason is not a correct explanation for assertion
• C. Assertion is correct, reason is incorrect
• D. Assertion is incorrect, reason is correct.

Answer 1

Answer: (B)

Let $x\in A-B$
$\Rightarrow x\in A$ and $x\notin B$
$\Rightarrow x\in A$ and $x\in B^{\prime }$
$\Rightarrow x\in B^{\prime }$
$\therefore A-B\subset B^{\prime }$
It is true $A\cap A^{\prime }=\varphi$ [by complement laws]
Hence, both Assertion and Reason are correct but Reason is not a correct explanation of Assertion.