JEE Main · 2011 · 10 Apr 2011 · Offline · Mathematical Reasoning *

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Consider the following statements

P : Suman is brilliant
Q : Suman is rich
R : Suman is honest
The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

(A) $\sim (Q \leftrightarrow (P_{\land} \sim R))$ ✓ Correct
(B) $\sim Q \leftrightarrow\sim P \land R$
(C) $\sim (P_{\land} \sim R) \leftrightarrow Q$
(D) $\sim P \land (Q \leftrightarrow\sim R)$

Answer: (A)

Solution

The statement reads

(P \land \sim R) \leftrightarrow Q

, with

P

for brilliant,

\sim R

for dishonest and

Q

for rich; this is the same as

Q \leftrightarrow (P \land \sim R)

. Its negation is simply

\sim (Q \leftrightarrow (P \land \sim R))

JEE Main · 2011 · 10 Apr 2011 · Offline · Single correct option

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JEE Main · 2011 · 10 Apr 2011 · Offline · Mathematical Reasoning *

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