Q75.Consider the following statements: P: Suman is brilliant Q: Suman is rich R: Suman is honest The negation of the statement, "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as (1) ~Q ↔~P ∨R (2) ~Q ↔P ∨~R (3) ~Q ↔P ∧~R (4) ~Q ↔~P ∧R
What This Question Tests
This question tests the understanding of logical connectives, particularly 'if and only if' and 'and', and the ability to apply rules for negation of compound statements to find an equivalent expression.
Concepts Tested
Formulas Used
Negation of P ↔ Q is ~(P ↔ Q) ≡ (P ∧ ~Q) ∨ (~P ∧ Q)
Negation of P ↔ Q ≡ P ↔ ~Q ≡ ~P ↔ Q
~(P ∧ Q) ≡ ~P ∨ ~Q
📚 NCERT Sections This Tests
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Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
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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.
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📋 Question Details
- Chapter
- Mathematical Reasoning
- Topic
- Logical Equivalence and Negation
- Year
- 2015
- Shift
- 11 Apr Online
- Q Number
- Q75
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 14: Mathematical Reasoning
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