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Let R be the relation on the set of positive integers such that aRb if and only if a and b are distinct and have a common divisor other than 1. Which one of the following statements about R is True?
  • a)
    R is symmetric and reflexive but not transitive
  • b)
    R is reflexive but not symmetric and not transitive
  • c)
    R is transitive but not reflexive and not symmetric
  • d)
    R is symmetric but not reflexive and not transitive
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let R be the relation on the set of positive integers such that aRb if...
R cannot be reflexive as 'a' and 'b' have to be distinct in aRb. R is symmetric if a and b have a common divisor, then b and a also have. R is not transitive as aRb and bRc doesn't mean aRc. For example 3 and 15 have common divisor, 15 and 5 have common divisor, but 3 and 5 don't have.
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Most Upvoted Answer
Let R be the relation on the set of positive integers such that aRb if...
Statement: R is the relation on the set of positive integers such that aRb if and only if a and b are distinct and have a common divisor other than 1.

To determine the properties of relation R, let's analyze each property separately.

Reflexivity:
Reflexivity means that every element in the set is related to itself. In this case, a positive integer a cannot be related to itself because the relation R is defined as aRb if and only if a and b are distinct. Therefore, relation R is not reflexive.

Symmetry:
Symmetry means that if a is related to b, then b is also related to a. Let's consider two positive integers, a and b, such that aRb. This means that a and b are distinct and have a common divisor other than 1. However, if we swap the positions of a and b, we still have distinct positive integers with a common divisor other than 1. Therefore, relation R is symmetric.

Transitivity:
Transitivity means that if a is related to b and b is related to c, then a is related to c. Let's consider three positive integers, a, b, and c, such that aRb and bRc. This means that a and b are distinct with a common divisor other than 1, and b and c are distinct with a common divisor other than 1. However, there is no guarantee that a and c are distinct or that they have a common divisor other than 1. Therefore, relation R is not transitive.

Conclusion:
Based on the analysis above, we can conclude that the correct statement about relation R is:
R is symmetric but not reflexive and not transitive. Therefore, the correct answer is option D.
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Let R be the relation on the set of positive integers such that aRb if and only if a and b are distinct and have a common divisor other than 1. Which one of the following statements about R is True?a)R is symmetric and reflexive but not transitiveb)R is reflexive but not symmetric and not transitivec)R is transitive but not reflexive and not symmetricd)R is symmetric but not reflexive and not transitiveCorrect answer is option 'D'. Can you explain this answer?
Question Description
Let R be the relation on the set of positive integers such that aRb if and only if a and b are distinct and have a common divisor other than 1. Which one of the following statements about R is True?a)R is symmetric and reflexive but not transitiveb)R is reflexive but not symmetric and not transitivec)R is transitive but not reflexive and not symmetricd)R is symmetric but not reflexive and not transitiveCorrect answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let R be the relation on the set of positive integers such that aRb if and only if a and b are distinct and have a common divisor other than 1. Which one of the following statements about R is True?a)R is symmetric and reflexive but not transitiveb)R is reflexive but not symmetric and not transitivec)R is transitive but not reflexive and not symmetricd)R is symmetric but not reflexive and not transitiveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be the relation on the set of positive integers such that aRb if and only if a and b are distinct and have a common divisor other than 1. Which one of the following statements about R is True?a)R is symmetric and reflexive but not transitiveb)R is reflexive but not symmetric and not transitivec)R is transitive but not reflexive and not symmetricd)R is symmetric but not reflexive and not transitiveCorrect answer is option 'D'. Can you explain this answer?.
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