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JEE Main 2011
Exam
JEE Main
Year
2011
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2011 · Mathematics · Mathematical Reasoning

Consider the following statements P : Suman is brilliant Q : Suman...

Consider the following statements P\mathrm{P} : Suman is brilliant Q : Suman is rich R\mathrm{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

Options

  1. A∼(Q↔(P∧∼R))\sim(\mathrm{Q} \leftrightarrow(\mathrm{P} \wedge \sim \mathrm{R}))
  2. B∼Q↔∼P∧R\sim Q \leftrightarrow \sim P \wedge R
  3. C∼(P∧∼R)↔Q\sim(P \wedge \sim R) \leftrightarrow Q
  4. D∼P∧(Q↔∼R)\sim P \wedge(Q \leftrightarrow \sim R)

Correct answer

A. ∼(Q↔(P∧∼R))\sim(\mathrm{Q} \leftrightarrow(\mathrm{P} \wedge \sim \mathrm{R}))

Step-by-step solution

∼\sim\left\{\left(P_{\wedge} \sim R\right) \leftrightarrow Q\right\}=\sim\left\{Q \leftrightarrow\left(P_{\wedge} \sim R\right)\right\}
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