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

  • question_answer 1) If \[\mathbf{n}\left( \mathbf{U} \right)=\mathbf{700},\mathbf{n}\left( \mathbf{A} \right)=\mathbf{200},\mathbf{n}\left( \mathbf{B} \right)=\mathbf{300}\], and \[\mathbf{n}\left( \mathbf{A}\cap \mathbf{B} \right)=\mathbf{100}\], then \[\mathbf{n}\left( \mathbf{A}'\cap \mathbf{B}' \right)=\]

    A) 400                              

    B) 350          

    C) 300                              

    D) 600

    Correct Answer: C

    Solution :

    [c] \[\therefore n\left( U \right)=700\] \[n\left( A \right)=200\] \[n\left( B \right)=300\] \[n\left( A\cap B \right)=100\] \[\because n\left( A\cup B \right)=n\left( A \right)+n\left( B \right)-n\left( A\cap B \right)\] \[=200+300-100=400\] Now, \[n\left( A'\cap B' \right)=n\left( A\cup B \right)'\] \[=n\left( U \right)-n\left( A\cup B \right)=700-400=300\] Hence, option is correct.

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