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JEE Main 20238 AprilMorning Shift
Exam
JEE Main
Year
2023
Date
8 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2023 · 8 April · Morning Shift · Mathematics · Mathematical Reasoning

Negation of (p → q) → (q → p) is

Negation of (p→q)→(q→p)is\left(p \to q\right) \to \left(q \to p\right) is

Options

  1. A(p )∨p\left(p ~\right) ∨ p
  2. Bq∧( p)q ∧ ( ~ p )
  3. C( q)∧p\left(~ q\right) ∧ p
  4. Dp∨( q)p ∨ \left(~ q\right)

Correct answer

B. q∧( p)q ∧ ( ~ p )

Step-by-step solution

We know that, A \to B ≡ ~ A ∨ B</p><p>Nowusingtheaboveformulawewillsolve,</p><p></p><p>Now using the above formula we will solve,</p><p>( p \to q ) \to ( q \to p )</p><p></p><p>≡ ~ \left(~ p ∨ q\right) ∨ \left(~ q ∨ p\right)

≡(p∧ q)∨( q∨p)</p><p>≡ \left(p ∧ ~ q\right) ∨ \left(~ q ∨ p\right)</p><p>≡ ~ q ∨ p

Now finding the negationof(p∨ q)weget,</p><p>negation of \left(p ∨ ~ q\right) we get,</p><p>~ \left(p ∨ ~ q\right)</p><p></p><p>≡ ~ p ∧ q

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