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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-6

  • question_answer
    If A and B be two non-empty sets, then \[\mathbf{A}\cap \left( \mathbf{A}\cup \mathbf{B} \right)'\]equals

    A)  A                                

    B)  \[\phi \]            

    C)  B                                

    D)  None of these

    Correct Answer: B

    Solution :

    [b] \[\because A\cap \left( A\cup B \right)\text{ }\!\!'\!\!\text{ }=A\cap \left( A'\cap B' \right)\] [By Demorgon's law] \[=\left( A\cap A' \right)\cap B'\] \[=\phi \cap B'=\phi \] Hence, option [b] is correct.


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