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QJEEM23Mab71c: JEE Main 2023 Mathematics - Class 11 JEEM23Mab71c Solution: The statement is equivalent to :

The statement ∼[p∨(∼(p∧q))]\sim[p \vee(\sim(p \wedge q))] is equivalent to :

Multiple Choice Options

  • A (∼(p∧q))∧q(\sim(p \wedge q)) \wedge q
  • B ∼(p∨q)\sim(p \vee q)
  • C (p∧q)∧(∼p)(p \wedge q) \wedge(\sim p)
  • D ∼(p∧q)\sim(p \wedge q)

Step-by-Step Verified Solution

pamp;qamp;p∧qamp;∼(p∧q)amp;p∨∼(p∧q)amp;∼[p∨∼(p∧q)]amp;p∨qamp;∼(p∨q)amp;(p∧q)∧(∼p)Tamp;Tamp;Tamp;Famp;Tamp;Famp;Tamp;Famp;FTamp;Famp;Famp;Tamp;Tamp;Famp;Tamp;Famp;FFamp;Tamp;Famp;Tamp;Tamp;Famp;Tamp;Famp;FFamp;Famp;Famp;Tamp;Tamp;Famp;Famp;Tamp;F\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline p & q & p \wedge q & \sim(p \wedge q) & \begin{array}{c}p \vee \sim \\(p \wedge q)\end{array} & \begin{array}{l}\sim[p \vee \sim \\(p \wedge q)]\end{array} & p \vee q & \begin{array}{l}\sim(p \\\vee q)\end{array} & \begin{array}{l}(p \wedge q) \wedge \\\quad(\sim p)\end{array} \\\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\\hline \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\\hline \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \\\hline \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \\\hline\end{array}

∴∼[p∨(∼(p∧q))]=∼p∧(p∧q)\therefore \sim[p \vee(\sim(p \wedge q))]=\sim p \wedge(p \wedge q)

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