Exams › JEE Main › Maths

Given that p and q are true statements while r is a false statement, which of the following is true?

1. (p∧q)∨r is false
2. (p∧q)⇒r is true
3. (p∨q)∧(p∨r) is true
4. (p⇒q)↔(p⇒r) is true

Correct answer: (p∨q)∧(p∨r) is true

Solution

The expression (p∨q)∧(p∨r) is true because both p and q are true, making p∨q true, and since p is true, p∨r is also true, resulting in the conjunction being true.

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 →