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VIT Engineering VIT Engineering Solved Paper-2011

  • question_answer
    If \[R\] be a relation from \[A=\{1,\,\,2,\,\,3,\,\,4\}\] to \[B=\{1,\,3,\,5\}\] such that \[(a,\,b)\in \,R\Leftrightarrow a<b,\]then \[RO{{R}^{-1}}\]is

    A)  \[\{(1,\,3),\,(1,\,5),\,(2,\,3),\,(2,\,5),\,(3,\,5),\,(4,\,5)\}\]

    B)  \[\{(3,\,1),\,(5,\,1),\,(3,\,2),\,(5,\,2),\,(5,\,3),\,(5,\,4)\}\]

    C)  \[\{(3,\,3),\,(3,\,5),\,(5,\,3),\,(5,\,5)\}\]

    D)  \[\{(3,\,3),\,(3,\,4),\,(3,\,4),\,(4,\,5)\}\]

    Correct Answer: C

    Solution :

    Given, A = {1, 2, 3, 4} and B = {1, 3, 5} \[\therefore \]         R = {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)} and \[{{R}^{-1}}\]= {(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)} Hence, \[RO{{R}^{-1}}=\]{(3, 3), (3, 5), (5, 3), (5, 5)}


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