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)

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

Answer 2

Negation of (P∧∼R)↔(∼Q)
⇒((P∧∼R)∧Q)∨(∼Q∧∼(P∧∼R))
⇒((P∧∼R)∧Q)∨(∼Q∧(∼P∨R))
Answer D is correct