JEE Main 2022 · 25 Jul · Shift 2 · Mathematics Q20

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MathematicsSingle correct+4 / -1Question 20 of 90

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 :

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

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

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

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

Answer and worked solution

Official answer: D

Statement $(P\wedge\sim R)\Leftrightarrow\sim Q$ . Its negation is $(P\wedge\sim R)\Leftrightarrow Q$ , i.e. $((P\wedge\sim R)\wedge Q)\vee(\sim Q\wedge(\sim P\vee R))$ .

(D)

Topics:Mathematical reasoning

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JEE Main 2022 · 25 Jul · Shift 2, Mathematics question 20