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Math Help - Question about sets

  1. #16
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    Re: Question about sets

    Quote Originally Posted by Plato View Post
    Correct. So the OP
    Is incorrect.
    OK, I see where I made a glitch. I was assuming that on a Venn diagram, the default way to represent A and B was ''partly separated'' and ''partly joined together'', but this isn't necessarily the case. When we only have a reunion and not an intersection, A and B don't have to be joined together at all, and the operation still works anyway.
    Last edited by Nombredor; December 3rd 2011 at 10:39 AM.
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  2. #17
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    Re: Question about sets

    Question about sets-abcd.png

    In this picture, how can we be sure that all possible combinations of 4 sets A-B-C-D are represented ?
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  3. #18
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    Re: Question about sets

    Quote Originally Posted by Nombredor View Post
    OK, I see where I made a glitch. I was assuming that on a Venn diagram, the default way to represent A and B was ''partly separated'' and ''partly joined together'', but this isn't necessarily the case. When we only have a reunion and not an intersection, A and B don't have to be joined together at all, and the operation still works anyway.
    Venn diagrams are a wonderful way to see outcomes.
    But they are a lousy way to prove anything.
    \begin{align*}(A\cup B^c)\cap (A\cup B)&=A\cup (B^c\cap B)\\&=A\cup (\emptyset)\\&= A \end{align*}
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