Exams › JEE Main › Maths

Let p be any proposition, t denote a tautology, and c denote a contradiction. Which of the following statements is not true?

1. p OR (NOT p) = c
2. p OR t = t
3. p AND t = p
4. p AND c = c

Correct answer: p OR (NOT p) = c

Solution

p OR (NOT p) is always true, so it equals t (a tautology), not c. Hence 'p OR (NOT p) = c' is the statement that is NOT true. The other three identities (p OR t = t, p AND t = p, p AND c = c) are all valid.

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 →