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JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    If A and B  are two given sets, then \[A\cap {{(A\cap B)}^{c}}\] is equal to                       [AMU 1998; Kurukshetra CEE 1999]

    A) A

    B) B

    C) \[\varphi \]

    D) \[A\cap {{B}^{c}}\]

    Correct Answer: D

    Solution :

    \[A\cap {{(A\cap B)}^{c}}=A\cap ({{A}^{c}}\cup {{B}^{c}})\]           = \[(A\cap {{A}^{c}})\cup (A\cap {{B}^{c}})\] = \[\varphi \cup (A\cap {{B}^{c}})=A\cap {{B}^{c}}\].


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