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SSC Quantitative Aptitude Number System and its Operations Question Bank Set Theory (II)

  • question_answer
    For non-empty subsets A, B and C of a set X such that \[A\cup B=B\cup C,\]which one of the following is the strongest inference that can be derived?

    A) \[A=B=C\]

    B) \[A\subseteq B=C\]

    C) \[A=B\subseteq C\]

    D) \[A\subseteq B\subseteq C\]

    Correct Answer: D

    Solution :

    [d] \[\because \]\[A\cup B=B\cap C\] From above, strong inference is \[A\subseteq B\subseteq C\] e.g. \[A=\{a\},\]\[B=\{a,b\},\]\[C=\{a,b,c\}\] \[\therefore \]      \[A\cup B=\{a,b\}\] and       \[B\cap C=\{a,\,b\}\]


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