Consider the following statements:P : Ramu is | vedclass

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(D) Given statements:$P$: Ramu is intelligent$Q$: Ramu is rich$R$: Ramu is not honestThe statement "Ramu is intelligent and honest if and only if Ramu

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$((P \wedge (\sim R)) \wedge Q) \vee ((\sim Q) \wedge ((\sim P) \vee R))$

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(D) Given statements:$P$: Ramu is intelligent$Q$: Ramu is rich$R$: Ramu is not honestThe statement "Ramu is intelligent and honest if and only if Ramu is not rich" is represented as $(P \wedge \sim R) \Leftrightarrow \sim Q$.The negation of the statement is $\sim[(P \wedge \sim R) \Leftrightarrow \sim Q]$.Using the identity $\sim(A \Leftrightarrow B) \equiv (A \wedge \sim B) \vee (B \wedge \sim A)$,where $A = (P \wedge \sim R)$ and $B = \sim Q$:$= ((P \wedge \sim R) \wedge \sim(\sim Q)) \vee (\sim Q \wedge \sim(P \wedge \sim R))$$= ((P \wedge \sim R) \wedge Q) \vee (\sim Q \wedge (\sim P \vee \sim(\sim R)))$$= ((P \wedge \sim R) \wedge Q) \vee (\sim Q \wedge (\sim P \vee R))$Thus,the correct option is $D$.

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:

Similar Questions

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Find the component statements of the following compound statement and check whether they are true or false.
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Consider the following statements:$P :$ Ramu is intelligent$Q :$ Ramu is rich$R :$ Ramu is not honestThe negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as: