QJEEM22Ma8c0e: JEE Main 2022 Mathematics - Class 11 JEEM22Ma8c0e Solution: Consider the following statements: P : Ramu is intelligent. Q : …

Question

Verified Solution • 2025–26 Session moderate

Consider the following statements:

P : Ramu is intelligent.

Q : Ramu is rich.

R : Ramu is not honest.

The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as:

Accepted Answer

P : Ramu is intelligent

Q : Ramu is rich

R : Ramu is not honest

Given statement, "Ramu is intelligent and honest if and only if Ramu is not rich"

$= (P \land \sim R) \Leftrightarrow \sim Q$

So, negation of the statement is

$\sim [(P \land \sim R) \Leftrightarrow \sim Q]$

$=\sim [{\sim (P \land \sim R) \lor \sim Q} \land {Q \lor (P \land \sim R)}]$

$= ((P \land \sim R) \land Q) \lor (\sim Q \land (\sim P \lor R))$

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