QJEEM22Ma0481: JEE Main 2022 Mathematics - Class 11 JEEM22Ma0481 Solution: Consider the following statements: A : Rishi is a judge. B :…

Question

Verified Solution • 2025–26 Session moderate

Consider the following statements:

A : Rishi is a judge.

B : Rishi is honest.

C : Rishi is not arrogant.

The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is

Accepted Answer

$∵$ Given statement is

(A $\land$ C) $\to$ B

Then its negation is

$\sim$ {(A $\land$ C) $\to$ B}

or $\sim$ { $\sim$ (A $\land$ C) $\lor$ B}

$∴$ (A $\land$ C) $\land$ ( $\sim$ B)

or ( $\sim$ B) $\land$ (A $\land$ C)

Step-by-Step Verified Solution