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Let R be the relation defined on the set of natural number N as aRb; a, b ∈ N, if a divides b.Then, which one of the following is correct?
  • a)
    R is reflexive only
  • b)
    R is symmetric only
  • c)
    R is transitive only
  • d)
    R is reflexive and transitive
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let R be the relation defined on the set of natural numberN as aRb; a,...
For reflexive aRa implies a divides a
So, R is reflexive.
For symmetric
aRb impliesa divides b
bRa impliesa divides a
which may not be possible.
So, R is not symmetric.
For transitive
aRb impliesa divides b implies b = ka bRc impliesb divides c implies c = lb Now, c = Ika
or a divides c implies aRc
or bRc implies cRa
Thus, R is transitive.
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Most Upvoted Answer
Let R be the relation defined on the set of natural numberN as aRb; a,...
Unfortunately, the second part of your question is missing. Could you please provide the complete definition of the relation R?
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Community Answer
Let R be the relation defined on the set of natural numberN as aRb; a,...
For reflexive aRa implies a divides a
So, R is reflexive.
For symmetric
aRb impliesa divides b
bRa impliesa divides a
which may not be possible.
So, R is not symmetric.
For transitive
aRb impliesa divides b implies b = ka bRc impliesb divides c implies c = lb Now, c = Ika
or a divides c implies aRc
or bRc implies cRa
Thus, R is transitive.
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Let R be the relation defined on the set of natural numberN as aRb; a, b ∈ N, if a divides b.Then, which one of the following is correct?a)R is reflexive onlyb)R is symmetric onlyc)R is transitive onlyd)R is reflexive and transitiveCorrect answer is option 'D'. Can you explain this answer?
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Let R be the relation defined on the set of natural numberN as aRb; a, b ∈ N, if a divides b.Then, which one of the following is correct?a)R is reflexive onlyb)R is symmetric onlyc)R is transitive onlyd)R is reflexive and transitiveCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let R be the relation defined on the set of natural numberN as aRb; a, b ∈ N, if a divides b.Then, which one of the following is correct?a)R is reflexive onlyb)R is symmetric onlyc)R is transitive onlyd)R is reflexive and transitiveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be the relation defined on the set of natural numberN as aRb; a, b ∈ N, if a divides b.Then, which one of the following is correct?a)R is reflexive onlyb)R is symmetric onlyc)R is transitive onlyd)R is reflexive and transitiveCorrect answer is option 'D'. Can you explain this answer?.
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