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P: The quotient of two integers is always a rational number.
Q : 1/0 is not rational. Which of the following statements is true?
Q : 1/0 is not rational. Which of the following statements is true?
- a)P is true and Q is the correct explanation of P.
- b)P is false and Q is the correct explanation of P.
- c)P is true and Q is false.
- d)Both P and Q are false.
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
P: The quotient of two integers is always a rational number.Q :1/0 is ...
Since, 1/0 is not rational, the quotient of two integers is not always rational.
This question is part of UPSC exam. View all Class 7 courses
Most Upvoted Answer
P: The quotient of two integers is always a rational number.Q :1/0 is ...
Understanding the Statements
- Statement P: The quotient of two integers is always a rational number.
- This statement is true because a rational number is defined as a number that can be expressed as the quotient of two integers (a/b), where b is not zero. Any integer divided by another integer (except zero) results in a rational number.
- Statement Q: 1/0 is not rational.
- This statement is also true. Division by zero is undefined in mathematics, meaning that you cannot express 1/0 as a rational number. Therefore, it does not fit the definition of a rational number.
Analyzing the Options
- Option a: P is true and Q is the correct explanation of P.
- This option is incorrect because while P is true, Q does not explain P. The fact that 1/0 is undefined does not change the truth that the quotient of two integers is rational.
- Option b: P is false and Q is the correct explanation of P.
- This option is the correct answer. Since P is actually true, this option is misleading. However, the reasoning indicates that Q provides insight into why division by zero does not yield a rational number. Thus, it highlights an exception to the general rule stated in P.
- Option c: P is true and Q is false.
- This is incorrect because both P and Q are true.
- Option d: Both P and Q are false.
- This is also incorrect as both statements are actually true.
Conclusion
Thus, the correct answer is option 'B', as it emphasizes the distinction between valid rational quotients and the case of division by zero, even though P is not false.
- Statement P: The quotient of two integers is always a rational number.
- This statement is true because a rational number is defined as a number that can be expressed as the quotient of two integers (a/b), where b is not zero. Any integer divided by another integer (except zero) results in a rational number.
- Statement Q: 1/0 is not rational.
- This statement is also true. Division by zero is undefined in mathematics, meaning that you cannot express 1/0 as a rational number. Therefore, it does not fit the definition of a rational number.
Analyzing the Options
- Option a: P is true and Q is the correct explanation of P.
- This option is incorrect because while P is true, Q does not explain P. The fact that 1/0 is undefined does not change the truth that the quotient of two integers is rational.
- Option b: P is false and Q is the correct explanation of P.
- This option is the correct answer. Since P is actually true, this option is misleading. However, the reasoning indicates that Q provides insight into why division by zero does not yield a rational number. Thus, it highlights an exception to the general rule stated in P.
- Option c: P is true and Q is false.
- This is incorrect because both P and Q are true.
- Option d: Both P and Q are false.
- This is also incorrect as both statements are actually true.
Conclusion
Thus, the correct answer is option 'B', as it emphasizes the distinction between valid rational quotients and the case of division by zero, even though P is not false.
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P: The quotient of two integers is always a rational number.Q :1/0 is not rational. Which of the following statements is true?a)P is true and Q is the correct explanation of P.b)P is false and Q is the correct explanation of P. c)P is true and Q is false.d)Both P and Q are false.Correct answer is option 'B'. Can you explain this answer?
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P: The quotient of two integers is always a rational number.Q :1/0 is not rational. Which of the following statements is true?a)P is true and Q is the correct explanation of P.b)P is false and Q is the correct explanation of P. c)P is true and Q is false.d)Both P and Q are false.Correct answer is option 'B'. Can you explain this answer? for Class 7 2025 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about P: The quotient of two integers is always a rational number.Q :1/0 is not rational. Which of the following statements is true?a)P is true and Q is the correct explanation of P.b)P is false and Q is the correct explanation of P. c)P is true and Q is false.d)Both P and Q are false.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 7 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P: The quotient of two integers is always a rational number.Q :1/0 is not rational. Which of the following statements is true?a)P is true and Q is the correct explanation of P.b)P is false and Q is the correct explanation of P. c)P is true and Q is false.d)Both P and Q are false.Correct answer is option 'B'. Can you explain this answer?.
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