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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : Sum of two irrational numbers is an irrational number.
Reason : Sum of a rational number and an irrational numbers is always an irrational number.
- a)Assertion (A) is true but reason (R) is false.
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'A'. Can you explain this answer?
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DIRECTION : In the following questions, a statement of assertion (A) i...
The correct answer is:
1. Assertion (A) is true but reason (R) is false.
Explanation:
Assertion (A): "Sum of two irrational numbers is an irrational number." This is not always true. For example, 2\sqrt{2}2 and −2-\sqrt{2}−2 are both irrational numbers, but their sum is 000, which is a rational number. Thus, the assertion is false.
Reason (R): "Sum of a rational number and an irrational number is always an irrational number." This is true because adding any non-zero rational number to an irrational number will not cancel out the irrational part, so the result is irrational.
So, the assertion is false, but the reason is true.
Most Upvoted Answer
DIRECTION : In the following questions, a statement of assertion (A) i...
Assertion: Sum of two irrational numbers is an irrational number.
Reason: Sum of a rational number and an irrational number is always an irrational number.
Explanation:
The given assertion states that the sum of two irrational numbers is an irrational number. To understand this, let's first define irrational numbers and then analyze the reason given.
Irrational Numbers:
An irrational number is a number that cannot be expressed as the ratio of two integers. They cannot be written as terminating or repeating decimals. Examples of irrational numbers include √2, √3, π, etc.
Reason Analysis:
The reason given states that the sum of a rational number and an irrational number is always an irrational number. To verify this, let's consider an example:
Let a be a rational number and b be an irrational number.
If we add a + b, where a is rational and b is irrational, the result will always be an irrational number. This can be proven by contradiction.
Assume that a + b is a rational number. This would mean that we can express it as the ratio of two integers, say p/q, where p and q are integers and q ≠ 0.
Then we have:
a + b = p/q
Rearranging the equation, we get:
b = p/q - a
Since a is rational, p/q - a is also rational.
But this contradicts the fact that b is an irrational number. Therefore, our assumption that a + b is rational is false.
Hence, we can conclude that the sum of a rational number and an irrational number is always an irrational number.
Conclusion:
Based on the above explanation, we can conclude that both the assertion and the reason are true, and the reason is the correct explanation of the assertion.
Therefore, the correct answer is option 'A' - Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Reason: Sum of a rational number and an irrational number is always an irrational number.
Explanation:
The given assertion states that the sum of two irrational numbers is an irrational number. To understand this, let's first define irrational numbers and then analyze the reason given.
Irrational Numbers:
An irrational number is a number that cannot be expressed as the ratio of two integers. They cannot be written as terminating or repeating decimals. Examples of irrational numbers include √2, √3, π, etc.
Reason Analysis:
The reason given states that the sum of a rational number and an irrational number is always an irrational number. To verify this, let's consider an example:
Let a be a rational number and b be an irrational number.
If we add a + b, where a is rational and b is irrational, the result will always be an irrational number. This can be proven by contradiction.
Assume that a + b is a rational number. This would mean that we can express it as the ratio of two integers, say p/q, where p and q are integers and q ≠ 0.
Then we have:
a + b = p/q
Rearranging the equation, we get:
b = p/q - a
Since a is rational, p/q - a is also rational.
But this contradicts the fact that b is an irrational number. Therefore, our assumption that a + b is rational is false.
Hence, we can conclude that the sum of a rational number and an irrational number is always an irrational number.
Conclusion:
Based on the above explanation, we can conclude that both the assertion and the reason are true, and the reason is the correct explanation of the assertion.
Therefore, the correct answer is option 'A' - Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers is an irrational number.Reason : Sum of a rational number and an irrational numbers is always an irrational number.a)Assertion (A) is true but reason (R) is false.b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer?
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers is an irrational number.Reason : Sum of a rational number and an irrational numbers is always an irrational number.a)Assertion (A) is true but reason (R) is false.b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers is an irrational number.Reason : Sum of a rational number and an irrational numbers is always an irrational number.a)Assertion (A) is true but reason (R) is false.b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers is an irrational number.Reason : Sum of a rational number and an irrational numbers is always an irrational number.a)Assertion (A) is true but reason (R) is false.b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer?.
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers is an irrational number.Reason : Sum of a rational number and an irrational numbers is always an irrational number.a)Assertion (A) is true but reason (R) is false.b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers is an irrational number.Reason : Sum of a rational number and an irrational numbers is always an irrational number.a)Assertion (A) is true but reason (R) is false.b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers is an irrational number.Reason : Sum of a rational number and an irrational numbers is always an irrational number.a)Assertion (A) is true but reason (R) is false.b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer?.
Solutions for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers is an irrational number.Reason : Sum of a rational number and an irrational numbers is always an irrational number.a)Assertion (A) is true but reason (R) is false.b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers is an irrational number.Reason : Sum of a rational number and an irrational numbers is always an irrational number.a)Assertion (A) is true but reason (R) is false.b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers is an irrational number.Reason : Sum of a rational number and an irrational numbers is always an irrational number.a)Assertion (A) is true but reason (R) is false.b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers is an irrational number.Reason : Sum of a rational number and an irrational numbers is always an irrational number.a)Assertion (A) is true but reason (R) is false.b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Sum of two irrational numbers is an irrational number.Reason : Sum of a rational number and an irrational numbers is always an irrational number.a)Assertion (A) is true but reason (R) is false.b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).d)Assertion (A) is false but reason (R) is true.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 9 tests.
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