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SSC Quantitative Aptitude Number System and its Operations Question Bank Set Theory (II)

  • question_answer
    If A, B and C are three sets and U is the universal set such that \[n\,(U)=700,\]\[n\,(A)=200,\]\[n\,(B)=300\]and \[n\,(A\cap B)=100,\] then what is the value of\[(A\cap B)\]?

    A) 100

    B) 200

    C) 300

    D) 400

    Correct Answer: C

    Solution :

    [c] Given that, \[n\,(U)=700,\]\[n\,(A)=200,\]\[n\,(B)=300\] and \[n\,(A\cap B)=100\] We know that, \[n\,(A\cup B)=n\,(A)+n\,(B)-n\,(A\cap B)\] \[=200+300-100=400\] Now, \[n\,(A'\cap B')=n\,(U)-n\,(A\cup B)\] \[=700-400=300\]


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