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Topic: Venn diagrams
Replies: 2   Last Post: Jan 23, 1995 4:02 AM

 Messages: [ Previous | Next ]
 DELBECQUE Yannick Posts: 37 Registered: 12/3/04
Venn diagrams
Posted: Jan 21, 1995 5:40 AM

Hi!

I know there is 2^n-1 disjoints set (without the empty set)
generated by n set (supposing that intersections are not empty). We
usually represent the situation with a venn diagram, the 2^-1 sets
coresponding to 2^n-1 areas in the diagram. I'm sure all of us have
seen those diagrams for cases n=2 and n=3. I recently discovered
one for n=4, whish represented each set with one region (and only one,
since it is possible draw diagrams where sets get splited by others... It
dosn't change the meaning of the diagram, but it is more interesting
considering those where numbers of regions=number of sets...).
Since then, I've tried to construct an equivallent diagram for n=5,
without succes. After a little thinking, I now conjecture that there is no
such representation. I've not been able to prove it (nor to get any conter
exemple by frinds or in math litterature...).

Can someone here solve this problem?

Date Subject Author
1/21/95 DELBECQUE Yannick
1/21/95 John Conway
1/23/95 DELBECQUE Yannick