11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-4

  • question_answer If \[\mathbf{A}=\left\{ \mathbf{1},\mathbf{2},\mathbf{3} \right\},\mathbf{B}=\left\{ \mathbf{3},\mathbf{4} \right\}\]and \[\mathbf{C}=\left\{ \mathbf{4},\mathbf{5},\mathbf{6} \right\}\]then \[\left( \mathbf{A}\times \mathbf{B} \right)\cap \left( \mathbf{B}\times \mathbf{C} \right)\]is equal to

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

    B) \[\left\{ \left( 4,4 \right),\left( 3,2 \right) \right\}\]

    C) \[\left\{ \left( 3,5 \right),\left( 3,4 \right) \right\}\]      

    D) \[\left\{ \left( 3,4 \right) \right\}\]

    Correct Answer: B

    Solution :

    [d]  \[A=\left\{ 1,2,3 \right\}\] \[B=\left\{ 3,4 \right\}\] \[C=\left\{ 4,5,6 \right\}\] \[A\times B=\left\{ \left( 1,3 \right),\left( 2,3 \right),\left( 3,3 \right),\left( 1,4 \right),\left( 2,4 \right),\left( 3,4 \right) \right\}\] \[B\times C=\left\{ \left( 3,4 \right),\left( 4,4 \right),\left( 3,5 \right),\left( 4,5 \right),\left( 3,6 \right),\left( 4,6 \right) \right\}\] \[\left( A\times B \right)\cap \left( B\times C \right)=\left\{ \left( 3,4 \right) \right\}\] Hence, option is correct.


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