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JEE Main & Advanced Sample Paper JEE Main Sample Paper-35

  • question_answer
    On the set N of all natural numbers, define the relation R by a Rb if and only if the greatest common divisor of a and b is 2, then R is

    A)  reflexive but not symmetric

    B)  symmetric only

    C)  reflexive and transitive

    D)  equivalence

    Correct Answer: B

    Solution :

    \[aRa\], then G.C.D of and a is a.             \[\therefore \] r is not reflexive.             (ii) \[aRb\Rightarrow bRa\] If G.C.D of a and b is 2, then G.C.D. of b and a is also 2. \[\Rightarrow \] R is symmetric. (iii) \[aRb,\,\,bRc\,aRc\]             e.g. \[4R2,\,\,2R8\,4R8\] \[\Rightarrow \] R is not transitive.


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