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Suppose there is a relation * between the positive numbers x and y given by x * y if and only if x ≤ y2. Then which one of the following is correct?
- a)* is reflexive but not transitive and symmetric
- b)* is transitive but not reflexive and symmetric
- c)* is symmetric and reflexive but not transitive
- d)* is symmetric and but not reflexive and transitive
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Suppose there is a relation * between the positive numbers x and y giv...
x and y are positive numbers.
x ≤ y2
x < x2
positive numbers.
Hence relation is reflexive.
Transitive -
Thus relation is not transitive.
Symmetric
1 ≤ (2)2 while 2
(I)2
Hence relation is not symmetric.
Thus x ≤ y2
positive numbers is reflexive, but not transitive and symmetric.
x ≤ y2
x < x2
positive numbers.Hence relation is reflexive.
Transitive -
Thus relation is not transitive.
Symmetric
1 ≤ (2)2 while 2
(I)2Hence relation is not symmetric.
Thus x ≤ y2
positive numbers is reflexive, but not transitive and symmetric.Most Upvoted Answer
Suppose there is a relation * between the positive numbers x and y giv...
Explanation:
Reflexivity:
- For a relation to be reflexive, every element of the set must be related to itself.
- In this case, if we take any positive number x, we have x * x since x ≤ x^2 is always true.
- Hence, the relation * is reflexive.
Transitivity:
- For a relation to be transitive, if x * y and y * z, then x * z must also hold true.
- Let's consider x = 2, y = 3, and z = 4.
- We have 2 * 3 and 3 * 4, but 2 * 4 is false since 2 is not less than or equal to 4^2.
- Therefore, the relation * is not transitive.
Symmetry:
- For a relation to be symmetric, if x * y, then y * x must also hold true.
- Since x * y is based on x ≤ y^2, it is not symmetric as the relation is not true for all pairs of x and y.
Therefore, the correct answer is option 'A' as the relation * is reflexive but not transitive and symmetric.
Reflexivity:
- For a relation to be reflexive, every element of the set must be related to itself.
- In this case, if we take any positive number x, we have x * x since x ≤ x^2 is always true.
- Hence, the relation * is reflexive.
Transitivity:
- For a relation to be transitive, if x * y and y * z, then x * z must also hold true.
- Let's consider x = 2, y = 3, and z = 4.
- We have 2 * 3 and 3 * 4, but 2 * 4 is false since 2 is not less than or equal to 4^2.
- Therefore, the relation * is not transitive.
Symmetry:
- For a relation to be symmetric, if x * y, then y * x must also hold true.
- Since x * y is based on x ≤ y^2, it is not symmetric as the relation is not true for all pairs of x and y.
Therefore, the correct answer is option 'A' as the relation * is reflexive but not transitive and symmetric.
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Suppose there is a relation * between the positive numbers x and y given by x * y if and only if x ≤ y2. Then which one of the following is correct?a)* is reflexive but not transitive and symmetricb)* is transitive but not reflexive and symmetricc)* is symmetric and reflexive but not transitived)* is symmetric and but not reflexive and transitiveCorrect answer is option 'A'. Can you explain this answer?
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Suppose there is a relation * between the positive numbers x and y given by x * y if and only if x ≤ y2. Then which one of the following is correct?a)* is reflexive but not transitive and symmetricb)* is transitive but not reflexive and symmetricc)* is symmetric and reflexive but not transitived)* is symmetric and but not reflexive and transitiveCorrect answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Suppose there is a relation * between the positive numbers x and y given by x * y if and only if x ≤ y2. Then which one of the following is correct?a)* is reflexive but not transitive and symmetricb)* is transitive but not reflexive and symmetricc)* is symmetric and reflexive but not transitived)* is symmetric and but not reflexive and transitiveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose there is a relation * between the positive numbers x and y given by x * y if and only if x ≤ y2. Then which one of the following is correct?a)* is reflexive but not transitive and symmetricb)* is transitive but not reflexive and symmetricc)* is symmetric and reflexive but not transitived)* is symmetric and but not reflexive and transitiveCorrect answer is option 'A'. Can you explain this answer?.
Suppose there is a relation * between the positive numbers x and y given by x * y if and only if x ≤ y2. Then which one of the following is correct?a)* is reflexive but not transitive and symmetricb)* is transitive but not reflexive and symmetricc)* is symmetric and reflexive but not transitived)* is symmetric and but not reflexive and transitiveCorrect answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Suppose there is a relation * between the positive numbers x and y given by x * y if and only if x ≤ y2. Then which one of the following is correct?a)* is reflexive but not transitive and symmetricb)* is transitive but not reflexive and symmetricc)* is symmetric and reflexive but not transitived)* is symmetric and but not reflexive and transitiveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose there is a relation * between the positive numbers x and y given by x * y if and only if x ≤ y2. Then which one of the following is correct?a)* is reflexive but not transitive and symmetricb)* is transitive but not reflexive and symmetricc)* is symmetric and reflexive but not transitived)* is symmetric and but not reflexive and transitiveCorrect answer is option 'A'. Can you explain this answer?.
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