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JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    Given \[n(U)=20\], \[n(A)=12\], \[n(B)=9\], \[n(A\cap B)=4\], where U is the universal set, A and B are subsets of U, then \[n({{(A\cup B)}^{C}})=\] [Kerala (Engg.) 2004]

    A) 17

    B) 9

    C) 11

    D) 3

    E) 16

    Correct Answer: D

    Solution :

    \[n(A\cup B)=n(A)+n(B)-n(A\cap B)=12+9-4=17\] Now, \[n({{(A\cup B)}^{C}})=n(U)-n(A\cup B)=20-17=3\].


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