JEE Main & Advanced Mathematics Set Theory and Relations Question Bank Critical Thinking

  • question_answer Let A = {1, 2, 3}, B = {1, 3, 5}. A relation \[R:A\to B\] is defined by R = {(1, 3), (1, 5), (2, 1)}. Then \[{{R}^{-1}}\] is defined by

    A) {(1,2), (3,1), (1,3), (1,5)}

    B) {(1, 2), (3, 1), (2, 1)}

    C) {(1, 2), (5, 1), (3, 1)}

    D) None of these

    Correct Answer: C

    Solution :

    \[(x,\,y)\in R\Leftrightarrow (y,\,x)\in {{R}^{-1}}\],   \[\therefore \] \[{{R}^{-1}}=\{(3,\,1),\,(5,\,1),\,(1,\,2)\}\].

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