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JEE Main & Advanced Mathematics Sets Question Bank Set theory

  • question_answer
    If   A = {2, 3, 4, 8, 10}, B = {3, 4, 5, 10, 12}, C = {4, 5, 6, 12, 14} then \[\left( A\text{ }\cap \text{ }B \right)\text{ }\cup \text{ }\left( A\text{ }\cap \text{ }C \right)\] is equal to 

    A) {3, 4, 10}

    B) {2, 8, 10}

    C) {4, 5, 6}

    D) {3, 5, 14}

    Correct Answer: A

    Solution :

    \[A\cap B=\{2,\,3,\,4,\,8,\,10\}\cap \{3,\,4,\,5,\,10,\,12\}\] \[=\{3,\,4,\,10\}\], \[A\cap C=\{4\}\]. \\[(A\cap B)\cup (A\cap C)=\{3,\,4,\,10\}\].


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