jee-main 2022 Q70

jee-main · India · session2_25jul_shift2 Proof True/False Justification

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:
(1) $((P \wedge (\sim R)) \wedge Q) \wedge ((\sim Q) \wedge ((\sim P) \vee R))$
(2) $((P \wedge R) \wedge Q) \vee ((\sim Q) \wedge ((\sim P) \vee (\sim R)))$
(3) $((P \wedge R) \wedge Q) \wedge ((\sim Q) \wedge ((\sim P) \vee (\sim R)))$
(4) $((P \wedge (\sim R)) \wedge Q) \vee ((\sim Q) \wedge ((\sim P) \wedge R))$

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:\\
(1) $((P \wedge (\sim R)) \wedge Q) \wedge ((\sim Q) \wedge ((\sim P) \vee R))$\\
(2) $((P \wedge R) \wedge Q) \vee ((\sim Q) \wedge ((\sim P) \vee (\sim R)))$\\
(3) $((P \wedge R) \wedge Q) \wedge ((\sim Q) \wedge ((\sim P) \vee (\sim R)))$\\
(4) $((P \wedge (\sim R)) \wedge Q) \vee ((\sim Q) \wedge ((\sim P) \wedge R))$

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