Let R be the relation on the set of positive integers such that aRb if and only if bear distinct and have a common divisor other than 1. Which one of the following statements about R is true?

GATE : Computer Science and IT

Let R be the relation on the set of positive integers such that aRb if and only if bear 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

Solution

D. R is symmetric but not reflexive and not transitive

Explanation

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.