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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

  • question_answer
        If the relation\[R:A\to B,\]where A = {1,2,3, 4} and B = {1,3,5} is defined by \[R=\{(x,y):x<y,x\in A,y\in B\},\],then\[{{R}^{-1}}oR\]is equal to

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

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

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

    D)  None of the above

    Correct Answer: C

    Solution :

                    \[\because \]\[R=\{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)\}\] and\[{{R}^{-1}}=\{(3,1),(5,1),(3,2),(5,2),(5,3),(5,4)\}\] Thus, \[{{R}^{-1}}oR=\{(3,5),(5,5),(3,3),(5,3)\}\]


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