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Math Help - Wikipedia error:Inclusion exclusion Theory

  1. #1
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    Wikipedia error:Inclusion exclusion Theory

    Image:Inclusion exclusion diagram.JPG - Wikipedia, the free encyclopedia

    For 4 events depicted, there should be 16-1=15 states.
    0001 to 1111.
    (we discount 0000 for the Venn diagram.)
    But I counted only 13.

    Is the diagram used to depict 4 events and their intersection wrong?
    Anybody got a better diagram?
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  2. #2
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    Last edited by chopet; November 4th 2007 at 04:08 AM.
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  3. #3
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    Posted my version above.

    The 4 events are depicted by their colours:
    Red, Blue, Black and Green.
    While Red, Blue and Black are the usual 3 circle Venn,
    I added Green...modified to resemble a doughnut with a hole in the middle and an extension outside of the 3 circles.

    The hole in the middle represent:
    P(Red \ Blue \ Black \ \overline{Green})

    The extension outside of the 3 circle represent:
    P( \overline{Red}\ \overline{Blue}\ \overline{Black}\ Green)

    Please feel free to comment. This model is useful for anyone who wants to understand the inclusion-exclusion theories and their derivatives, e.g. Waring's Theorem, and also to visualise the De Montmort's Problem of Coincidences better.
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