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Math Help - Disjoint sets

  1. #1
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    Disjoint sets

    How can we show that A/B, B/A and A and(Cant do the upside down u symbol) B are disjoint sets?

    Thanks for your help in advance
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  2. #2
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    Quote Originally Posted by adam_leeds View Post
    How can we show that A/B, B/A and A and(Cant do the upside down u symbol) B are disjoint sets?
    Is your task to show that A\setminus B,~B\setminus A,~\&~A\cap B are pair-wise disjoint?
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  3. #3
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    Quote Originally Posted by Plato View Post
    Is your task to show that A\setminus B,~B\setminus A,~\&~A\cap B are pair-wise disjoint?
    This is what im confused about as well it says :
    Show that A\setminus B,~B\setminus A,~\&~A\cap B are disjoint sets
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  4. #4
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    Quote Originally Posted by adam_leeds View Post
    This is what im confused about as well it says :
    Show that A\setminus B,~B\setminus A,~\&~A\cap B are disjoint sets
    Say that x\in A\setminus B that means that x\in A,~x\notin B.
    Thus is it at all possible for x\in B\setminus A,\text{ or }x\in A\cap B?
    Last edited by Plato; December 24th 2009 at 10:46 AM.
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  5. #5
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    If you want to show that 3 sets A,B,C are pairwise disjoint then you can show the following implications: x\in A \Rightarrow x\notin B, x\in B\Rightarrow x\notin C, x\in C\Rightarrow x\notin A

    For example: x\in A\setminus B \Rightarrow x\notin B \Rightarrow x\notin B\setminus A. Thus A\setminus B and B\setminus A are disjoint sets.
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  6. #6
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    thank you im giving up for now as its xmas tomorrow

    merry xmas everyone
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