Q70.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 true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true
What This Question Tests
This question assesses the ability to determine logical equivalence between compound statements involving biconditional and negation, and to identify if a statement is a tautology, typically by using truth tables or known logical equivalences.
Concepts Tested
Formulas Used
p ↔ q ≡ (p → q) ∧ (q → p)
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
~(~p) ≡ p
📚 NCERT Sections This Tests
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
14.1 — In An N-Type Silicon, Which Of The Following Statement Is True:
Physics Class 12 · Chapter 14
14.1 In an n-type silicon, which of the following statement is true: (a) Electrons are majority carriers and trivalent atoms are the dopants. (b) Electrons are minority carriers and pentavalent atoms are the dopants. (c) Holes are minority carriers and pentavalent atoms are the dopants. (d) Holes are majority carriers and trivalent atoms are the dopants.
7.22 — Give Reason For The Higher Boiling Point Of Ethanol In Comparison To
Chemistry Class 12 · Chapter 7
7.22 Give reason for the higher boiling point of ethanol in comparison to methoxymethane. 223 Alcohols, Phenols and Ethers Reprint 2025-26
📋 Question Details
- Chapter
- Mathematical Reasoning
- Topic
- Logical equivalence and tautology
- Year
- 2009
- Shift
- Unknown
- Q Number
- Q70
- Type
- Assertion Reasoning
- NCERT Ref
- Class 11 Mathematics Ch 14: Mathematical Reasoning
More from this Chapter
Q82.Let p be the statement " x is an irrational number", q be the statement " y is a transcendental number", and r be the statement " x is a rational number iff y is a transcendental number". Statement −1 : r is equivalent to either q or p Statement −2 : r is equivalent to ∼(p ↔∼q). (1) Statement −1 is false, Statement −2 is true (2) Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1 (3) Statement −1 is true, Statement −2 is true; (4) Statement −1 is true, Statement −2 is false. Statement −2 is not a correct explanation for Statement −1.
Q83.The statement p →(q →p) is equivalent to (1) p →(p →q) (2) p →(p ∨q) (3) p →(p ∧q) (4) p →(p ↔q)
Q73.Let S be a non-empty subset of R. Consider the following statement: P : There is a rational number x ∈S such that x > 0. Which of the following statements is the negation of the statement P ? JEE Main 2010 JEE Main Previous Year Paper (1) There is no rational number x ∈S such that (2) Every rational number x ∈S satisfies x ≤0 x ≤0 (3) x ∈S and x ≤0 ⇒x is not rational (4) There is a rational number x ∈S such that x ≤0
Q72.If the mean deviation about the median of the numbers a, 2a, … , 50a is 50 , then |a| equals (1) 3 (2) 4 (3) 5 (4) 2