Exams › JEE Main › Maths

Statement-1: ~(p ↔ ~q) is equivalent to p ↔ q. Statement-2: ~(p ↔ ~q) is a tautology.

1. Statement-1 is true, Statement-2 is true
2. Statement-1 is true, Statement-2 is false
3. Statement-1 is false, Statement-2 is true
4. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

Correct answer: Statement-1 is true, Statement-2 is false

Solution

Statement-1 is true because the negation of a biconditional can be shown to be equivalent to the original biconditional when both sides are negated. However, Statement-2 is false because ~(p ↔ ~q) is not always true for all truth values of p and q, thus it is not a tautology.

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 →