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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 17

  • question_answer
    Let \[A=\{1, 2, 3, 4\}\]. The number of different ordered pairs \[(B,C)\] that can be formed such that \[B\subseteq A,\] \[C\subseteq A\] and \[B\cap C\] is empty, is

    A) \[{{2}^{4}}\]                    

    B)        \[{{3}^{4}}\]      

    C) \[{{4}^{3}}\]                    

    D)        None of these

    Correct Answer: B

    Solution :

        [b] For each element of set A, there are 3 possibilities i.e.,
    (i) element of B but not element of C
    (ii) element of C but not element of B
    (iii) neither element of B nor element of C
    So, number of ways\[={{3}^{4}}\]


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