11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-3

  • question_answer
    If A, B and C are non-empty subsets of a set, then \[\left( \mathbf{A}-\mathbf{B} \right)\cup \left( \mathbf{B}-\mathbf{A} \right)\] equal

    A)  \[\left( A\cup B \right)-B\]          

    B)  \[A-\left( A\cap B \right)\]

    C)  \[\left( A\cup B \right)-\left( A\cap B \right)\]          

    D)  \[\left( A\cap B \right)\cup \left( A\cup B \right)\]

    Correct Answer: C

    Solution :

    [c] \[\because \left( A-B \right)\cup \left( B-A \right)\] [Which is symmetric difference] \[=\left\{ A-A\cap B) \right\}\cup \left\{ B-\left( A\cap B \right) \right\}=\left( A\cup B \right)-\left( A\cap B \right)\]

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