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J & K CET Engineering J and K - CET Engineering Solved Paper-2004

  • question_answer
    Let R be the relation on the set R of all real  numbers defined by aRb if \[|a-b|\le 1,\]then R is

    A)  Reflexive and symmetric

    B)  Symmetric only

    C)  Transitive only

    D)  Anti symmetric only

    Correct Answer: A

    Solution :

    Now, aRa is \[|a-a|=0\le 1,\] which is true. \[\therefore \]   It is reflexive Now,  aRb, \[|a-b|\le 1\,\,\,\,\Rightarrow \,\,\,|b-a|\le 1\] \[\Rightarrow \] \[aRb\] \[\Rightarrow \]\[bRa\] \[\therefore \] It is symmetric.


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