GATE | GATE-CS-2015 (Set 2) | Question 26
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
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.
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