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Thread: Set help appreciated

  1. #1
    Jul 2008

    Smile Set help appreciated

    Here is the question at this link: Yfrog Image :

    So here's what I've done so far: I know the A with the little hat on top means everything outside of A ie the universe. Now I know that A u B with the hat over all of that is A n B with hats over A and B only. So there's now A with 2 hats? Does that just mean A? If so, then it is A n B with a hat only over B. My answer to that is an empty set. Please help! I've done something wrong here!

    Thanks in advance.
    Last edited by brumby_3; Jul 26th 2010 at 07:00 PM.
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  2. #2
    Super Member

    May 2006
    Lexington, MA (USA)
    Hello, brumby_3!

    Prove that: .$\displaystyle \overline{\left(\,\overline{A} \cup B\right)} \cup B \;=\;A \cup B$

    $\displaystyle \begin{array}{cccc}
    1. & \overline{\left(\overlie{A} \cup B\right)} \cup B &\quad& \text{Given} \\ \\
    2. & \left(\, \overline{\overline A}} \cap \overline{B}\right) \cup B &\quad& \text{DeMorgan} \\ \\
    3. & \left(A \cap \overline{B}\right) \cup B &\quad & \text{Double negative} \\ \\
    4. & (A \cup B) \cap (\overline{B} \cup B) &\quad& \text{Distributive} \\ \\
    5. & (A \cup B) \cap U &\quad& X\cup \overline{X} \,=\,U \\ \\
    6. & A \cup B &\quad& X \cap U \,=\,X

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