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A relation R is defined on the set N of natural numbers as xRy ⇒ x2 − 4xy + 3y2 = 0. Then which one of the following is correct?
  • a)
    R is reflexive and symmetric, but not transitive
  • b)
    R is reflexive and transitive, but not symmetric
  • c)
    R is reflexive, symmetric and transitive
  • d)
    R is reflexive, but neither symmetric nor transitive
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A relation R is defined on the set N of natural numbers as xRy⇒ x...

So, R is not transitive.
Hence, R is neither symmetric nor  transitive, but reflexive.
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Most Upvoted Answer
A relation R is defined on the set N of natural numbers as xRy⇒ x...
A relation R is defined on the set N of natural numbers as xRy if and only if x is divisible by y (i.e., x is a multiple of y).
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A relation R is defined on the set N of natural numbers as xRy⇒ x2 − 4xy+ 3y2 = 0. Then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is reflexive and transitive, but not symmetricc)R is reflexive, symmetric and transitived)R is reflexive, but neither symmetric nor transitiveCorrect answer is option 'D'. Can you explain this answer?
Question Description
A relation R is defined on the set N of natural numbers as xRy⇒ x2 − 4xy+ 3y2 = 0. Then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is reflexive and transitive, but not symmetricc)R is reflexive, symmetric and transitived)R is reflexive, but neither symmetric nor transitiveCorrect answer is option 'D'. 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 A relation R is defined on the set N of natural numbers as xRy⇒ x2 − 4xy+ 3y2 = 0. Then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is reflexive and transitive, but not symmetricc)R is reflexive, symmetric and transitived)R is reflexive, but neither symmetric nor transitiveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A relation R is defined on the set N of natural numbers as xRy⇒ x2 − 4xy+ 3y2 = 0. Then which one of the following is correct?a)R is reflexive and symmetric, but not transitiveb)R is reflexive and transitive, but not symmetricc)R is reflexive, symmetric and transitived)R is reflexive, but neither symmetric nor transitiveCorrect answer is option 'D'. Can you explain this answer?.
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