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Let R be a relation on the set N of natural numbers defined by 'nRM n is a factor of m'. Then which one of the following is correct?
- a)R is reflexive, symmetric but not transitive
- b)R is transitive, symmetric but not reflexive
- c)R is reflexive, transitive but not symmetric
- d)R is an equivalence relation
Correct answer is option 'C'. Can you explain this answer?
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Let R be a relation on the set N of natural numbers defined by 'nR...
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Let R be a relation on the set N of natural numbers defined by 'nR...
Explanation:
To determine the properties of the relation R, let's analyze each property one by one.
Reflexive:
A relation R is reflexive if every element in the set is related to itself. In this case, we need to check if every natural number is a factor of itself.
Since every number is a factor of itself (n is always a factor of n), the relation R is reflexive.
Symmetric:
A relation R is symmetric if for every pair (a, b) in R, the pair (b, a) is also in R. In this case, we need to check if for every pair (n, m) in R, the pair (m, n) is also in R.
If n is a factor of m, it means that m is divisible by n. However, if m is divisible by n, it does not necessarily mean that n is a factor of m. Therefore, the relation R is not symmetric.
Transitive:
A relation R is transitive if for every pair (a, b) and (b, c) in R, the pair (a, c) is also in R. In this case, we need to check if for every pair (n, m) and (m, p) in R, the pair (n, p) is also in R.
If n is a factor of m and m is a factor of p, then n is a factor of p. Therefore, the relation R is transitive.
Equivalence Relation:
An equivalence relation is a relation that is reflexive, symmetric, and transitive. Since the relation R is reflexive and transitive but not symmetric, it does not satisfy all the properties of an equivalence relation.
Conclusion:
Based on the analysis above, the correct option is C) R is reflexive, transitive but not symmetric.
To determine the properties of the relation R, let's analyze each property one by one.
Reflexive:
A relation R is reflexive if every element in the set is related to itself. In this case, we need to check if every natural number is a factor of itself.
Since every number is a factor of itself (n is always a factor of n), the relation R is reflexive.
Symmetric:
A relation R is symmetric if for every pair (a, b) in R, the pair (b, a) is also in R. In this case, we need to check if for every pair (n, m) in R, the pair (m, n) is also in R.
If n is a factor of m, it means that m is divisible by n. However, if m is divisible by n, it does not necessarily mean that n is a factor of m. Therefore, the relation R is not symmetric.
Transitive:
A relation R is transitive if for every pair (a, b) and (b, c) in R, the pair (a, c) is also in R. In this case, we need to check if for every pair (n, m) and (m, p) in R, the pair (n, p) is also in R.
If n is a factor of m and m is a factor of p, then n is a factor of p. Therefore, the relation R is transitive.
Equivalence Relation:
An equivalence relation is a relation that is reflexive, symmetric, and transitive. Since the relation R is reflexive and transitive but not symmetric, it does not satisfy all the properties of an equivalence relation.
Conclusion:
Based on the analysis above, the correct option is C) R is reflexive, transitive but not symmetric.
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Let R be a relation on the set N of natural numbers defined by 'nRM n is a factor of m'.Then which one of the following is correct?a)R is reflexive, symmetric but not transitiveb)R is transitive, symmetric but not reflexivec)R is reflexive, transitive but not symmetricd)R is an equivalence relationCorrect answer is option 'C'. Can you explain this answer?
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Let R be a relation on the set N of natural numbers defined by 'nRM n is a factor of m'.Then which one of the following is correct?a)R is reflexive, symmetric but not transitiveb)R is transitive, symmetric but not reflexivec)R is reflexive, transitive but not symmetricd)R is an equivalence relationCorrect answer is option 'C'. 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 Let R be a relation on the set N of natural numbers defined by 'nRM n is a factor of m'.Then which one of the following is correct?a)R is reflexive, symmetric but not transitiveb)R is transitive, symmetric but not reflexivec)R is reflexive, transitive but not symmetricd)R is an equivalence relationCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be a relation on the set N of natural numbers defined by 'nRM n is a factor of m'.Then which one of the following is correct?a)R is reflexive, symmetric but not transitiveb)R is transitive, symmetric but not reflexivec)R is reflexive, transitive but not symmetricd)R is an equivalence relationCorrect answer is option 'C'. Can you explain this answer?.
Let R be a relation on the set N of natural numbers defined by 'nRM n is a factor of m'.Then which one of the following is correct?a)R is reflexive, symmetric but not transitiveb)R is transitive, symmetric but not reflexivec)R is reflexive, transitive but not symmetricd)R is an equivalence relationCorrect answer is option 'C'. 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 Let R be a relation on the set N of natural numbers defined by 'nRM n is a factor of m'.Then which one of the following is correct?a)R is reflexive, symmetric but not transitiveb)R is transitive, symmetric but not reflexivec)R is reflexive, transitive but not symmetricd)R is an equivalence relationCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be a relation on the set N of natural numbers defined by 'nRM n is a factor of m'.Then which one of the following is correct?a)R is reflexive, symmetric but not transitiveb)R is transitive, symmetric but not reflexivec)R is reflexive, transitive but not symmetricd)R is an equivalence relationCorrect answer is option 'C'. Can you explain this answer?.
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