JEE Main & Advanced Mathematics Sets Question Bank Critical Thinking

  • question_answer Let a relation R be defined by R = {(4, 5); (1, 4); (4, 6);     (7, 6); (3, 7)} then \[{{R}^{-1}}oR\] is

    A) {(1, 1), (4, 4), (4, 7), (7, 4), (7, 7), (3, 3)}

    B) {(1, 1), (4, 4), (7, 7), (3, 3)}

    C) {(1, 5), (1, 6), (3, 6)}

    D) None of these

    Correct Answer: A

    Solution :

    We first find\[{{R}^{-1}},\] we have \[{{R}^{-1}}=\{(5,\,4);\,(4,\,1);\,(6,\,4);\,(6,\,7);\,(7,\,3)\}\]. We now obtain the elements of \[{{R}^{-1}}oR\] we first pick the element of R and then of \[{{R}^{-1}}\]. Since \[(4,\,5)\in R\] and \[(5,\,4)\in {{R}^{-1}}\], we have \[(4,\,4)\in {{R}^{-1}}oR\] Similarly, \[(1,\,4)\in R,\,(4,\,1)\in {{R}^{-1}}\Rightarrow \,(1,\,1)\in {{R}^{-1}}oR\] \[(4,\,6)\in R,\,(6,\,4)\in {{R}^{-1}}\Rightarrow \,(4,\,4)\in {{R}^{-1}}oR,\]   \[(4,\,6)\in R,\,(6,\,7)\in {{R}^{-1}}\Rightarrow \,(4,\,7)\in {{R}^{-1}}oR\] \[(7,\,6)\in R,\,(6,\,4)\in {{R}^{-1}}\Rightarrow \,(7,\,4)\in {{R}^{-1}}oR,\]        \[(7,\,6)\in R,\,(6,\,7)\in {{R}^{-1}}\Rightarrow \,(7,\,7)\in {{R}^{-1}}oR\] \[(3,\,7)\in R,\,(7,\,3)\in {{R}^{-1}}\Rightarrow \,(3,\,3)\in {{R}^{-1}}oR,\] Hence,\[{{R}^{-1}}oR=\]{(1, 1); (4, 4); (4, 7); (7, 4), (7, 7); (3, 3)}.


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