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Negation of the statement p→(q ∨ r) is
  • a)
    ∼p→∼(q ∨ r)
  • b)
    ∼p→∼(q ∧ r)
  • c)
    (q ∨ r)→ p
  • d)
    p ∧ (∼q ∧∼r )
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Negation of the statementp→(q ∨ r)isa)∼p→∼(q ∨...
The correct option is D p ∧ (∼q ∧∼r)
We know that, ∼(p → q)≡ p ∧ (∼q)
Also, negation of (q ∨ r) is (∼q∧∼r)
So, ∼(p→(q ∨ r))≡ p ∧(∼q∧∼r)
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Most Upvoted Answer
Negation of the statementp→(q ∨ r)isa)∼p→∼(q ∨...

Explanation:

Given Statement: p → (q ∨ r)

Negation: ¬(p → (q ∨ r))


  • Using the rule ¬(p → q) ≡ p ∧ ¬q:



¬(p → (q ∨ r)) ≡ p ∧ ¬(q ∨ r)



  • Using De Morgan's Law ¬(p ∨ q) ≡ ¬p ∧ ¬q:



p ∧ ¬(q ∨ r) ≡ p ∧ (¬q ∧ ¬r)



  • Final Answer:



p ∧ (¬q ∧ ¬r)


Therefore, the negation of the statement p → (q ∨ r) is option D) p ∧ (¬q ∧ ¬r).
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Question Description
Negation of the statementp→(q ∨ r)isa)∼p→∼(q ∨ r)b)∼p→∼(q ∧ r)c)(q ∨ r)→ pd)p ∧ (∼q ∧∼r )Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Negation of the statementp→(q ∨ r)isa)∼p→∼(q ∨ r)b)∼p→∼(q ∧ r)c)(q ∨ r)→ pd)p ∧ (∼q ∧∼r )Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Negation of the statementp→(q ∨ r)isa)∼p→∼(q ∨ r)b)∼p→∼(q ∧ r)c)(q ∨ r)→ pd)p ∧ (∼q ∧∼r )Correct answer is option 'D'. Can you explain this answer?.
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