Verified Solution • 2025–26 Session moderate

QJEEM23Mac809: JEE Main 2023 Mathematics - Class 11 JEEM23Mac809 Solution: Negation of is :

Negation of (p⇒q)⇒(q⇒p)(p \Rightarrow q) \Rightarrow(q \Rightarrow p) is :

Multiple Choice Options

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

Step-by-Step Verified Solution

Given: (p→q)→(q→p)(p \rightarrow q) \rightarrow(q \rightarrow p)

Negation of above statement is :

amp;∼[(p→q)→(q→p)]amp;≡∼[∼p→q∧q→p]amp;≡p→q∧∼q→pamp;≡∼p∨q∧q∧∼p]amp;≡q∧(∼p)\begin{aligned}& \sim[(p \rightarrow q) \rightarrow(q \rightarrow p)] \\\\& \equiv \sim[\sim p \rightarrow q \wedge q \rightarrow p] \\\\& \equiv p \rightarrow q \wedge \sim q \rightarrow p \\\\& \equiv \sim p \vee q \wedge q \wedge \sim p] \\\\& \equiv q \wedge(\sim p)\end{aligned}

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