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JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    If A, B, C are three sets, then \[A\text{ }\cap \text{ }\left( B~\text{ }\cup \text{ }C \right)\] is equal to

    A) \[\left( A\text{ }\cup \text{ }B \right)\text{ }\cap \text{ }\left( A\text{ }\cup \text{ }C \right)\]

    B) \[\left( A\text{ }\cap \text{ }B \right)\text{ }\cup \text{ }\left( A\text{ }\cap \text{ }C \right)\]

    C) \[\left( A\text{ }\cup \text{ }B \right)\text{ }\cup \text{ }\left( A\text{ }\cup \text{ }C \right)\]

    D) None of these

    Correct Answer: B

    Solution :

    From Distributive law, \[A\cap (B\cup C)=(A\cap B)\cup (A\cap C)\].


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