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  • Consider the following statements : : Ramu is intelligent.

Consider the following statements :
\mathrm{P} : Ramu is intelligent.
\mathrm{Q} : Ramu is rich.
\mathrm{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 :
 

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

\mathrm{((P \wedge(\sim R)) \wedge Q) \vee((\sim Q) \wedge((\sim P) \vee R))}


Answers (1)

best_answer

Given statement is \mathrm{(p \wedge \sim r) \longleftrightarrow \sim q}

\mathrm{\equiv((p \wedge \sim r) \rightarrow \sim q) \wedge(\sim q \rightarrow(p \wedge \sim r))}\\

\mathrm{\equiv(\sim(p \wedge \sim r) \vee \sim q) \wedge(q \vee(p \wedge \sim r))}

It's negation is

\mathrm{\sim(\sim(p \wedge \sim r) \vee \wedge q) \vee \sim(q \vee(p \wedge \sim r)) } \\

\mathrm{\equiv ((p \wedge \sim r) \wedge q) \vee(\sim q \wedge \sim(p \wedge \sim r))}

Hence correct option is 4

Posted by

Devendra Khairwa

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