# Wikipedia error:Inclusion exclusion Theory

• Oct 27th 2007, 07:06 AM
chopet
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?
• Oct 27th 2007, 07:30 AM
chopet
• Oct 27th 2007, 07:36 AM
chopet
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.