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JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    If A and B are two sets, then \[A\cap (A\cup B{)}'\] is equal to

    A) A

    B) B

    C) \[\varphi \]

    D) None of these

    Correct Answer: C

    Solution :

    \[A\cap (A\cup B{)}'=A\cap ({A}'\cap {B}')\], \[(\because (A\cup B{)}'={A}'\cap {B}'\,)\]         \[=(A\cap {A}')\cap {B}'\],      (by associative law)         \[=\varphi \cap {B}'\],                 \[(\because A\cap {A}'=\varphi )\]         \[=\varphi \].


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