Exams › JEE Main › Maths

What is the negation of the statement p → (q ∧ r)?

1. ~p → ~(q ∧ r)
2. ~p ∨ (q ∧ r)
3. (q ∧ r) → p
4. p ∧ (~q ∨ ~r)

Correct answer: p ∧ (~q ∨ ~r)

Solution

Negating an implication: ~(p -> (q ∧ r)) = p ∧ ~(q ∧ r) = p ∧ (~q ∨ ~r).

Related JEE Main Maths questions

• Let T(k) denote the claim that 1 + 3 + 5 +... + (2k - 1) = k² + 10. Which statement below is correct?
• Let S(k) denote the sum 1 + 3 + 5 +... + (2k - 1), and suppose it is given by 3 + k². Which statement below is true?
• For every natural number n, which of the following inequalities is true?
• Let p, q, and r be arbitrary logical propositions. Which of the following equivalences is correct?
• The proposition ~(p → q) → [(~p) ∨ (~q)] is best classified as
• For integers m and n, each exceeding 1, let the statements be: P: m is a divisor of n, Q: m is a divisor of n², and R: m is a prime number. Which of the following implications is true?

⚔️ Practice JEE Main Maths free + battle 1v1 →