Venn Diagram

using circles, can you draw a Venn Diagram of order 4?

I do not think so. Combinations(4, 2) = 6, which looks like a problem. If it can be done, the diagram is not likely to be symmetric like the order 3 diagram.

No, i'm pretty sure u can't
Consider the normal 3-circle thing. now, look at only the union parts (A&B, A&C, B&C, A&B&C). You get some flower-thing, with three petals.
Consider two of the petals (A&B, and A&C). If D completely covered one of them, then there would be no (A&B&!C&!D) or (A&C&!B&!D) part left.
=> some parts of these two petals must not be within D, some also must be.
However, this means that both:
a) D covers some of B&C which A doesn't
b) D must have a smaller radius than A

combining the two, you get that there is no section of D that is by itself. (I think)

=> impossible

Also, # of sections actually = 2^4=16, with each circle in 8 sections

A venn diagram with four circles is imposible in 2D, but it can be done in 3D.

Hypothesis: max possible venn diagram size = dimension+1

interesting hypothesis...