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venn diagrams
Posted:
Jan 21, 1995 10:40 AM


Hi! I know there is 2^n1 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^n1 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?



