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JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    Let \[n(U)=700,\,n(A)=200,\,n(B)=300\] and \[n(A\cap B)=100,\] then \[n({{A}^{c}}\cap {{B}^{c}})=\] [Kurukshetra CEE 1999]

    A) 400

    B) 600

    C) 300

    D) 200

    Correct Answer: C

    Solution :

    \[n({{A}^{c}}\cap {{B}^{c}})\] = n[(A È B)c]  = \[n(U)-n(A\cup B)\] = \[n(U)-[n(A)+n(B)-n(A\cap B)]\] = 700 - [200 + 300 - 100] = 300.


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