Question

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 :

• A. $(( P \wedge(\sim R )) \wedge Q ) \wedge((\sim Q ) \wedge((\sim P ) \vee R ))$
• B. $(( P \wedge R ) \wedge Q ) \vee((\sim Q ) \wedge((\sim P ) \vee(\sim R )))$
• C. $(( P \wedge R ) \wedge Q ) \wedge((\sim Q ) \wedge((\sim P ) \vee(\sim R )))$
• D. $(( P \wedge(\sim R )) \wedge Q ) \vee((\sim Q ) \wedge((\sim P ) \vee R ))$

Answer 1

Answer: (D)

Negation of $( P \wedge \sim R ) \leftrightarrow(\sim Q )$
$\Rightarrow(( P \wedge \sim R ) \wedge Q ) \vee(\sim Q \wedge \sim( P \wedge \sim R ))$
$ \Rightarrow(( P \wedge \sim R ) \wedge Q ) \vee(\sim Q \wedge(\sim P \vee R ))$
Answer $D$ is correct