In the picture below I managed to draw a Venn diagram for 4 sets with ellipses delineating each of the 4 sets ($A,B,C,D$).
Is it possible to draw a Venn diagram on the plane for an arbitrary number of sets, using convex domains for each of the participating sets?
Jutst to be clear: a Venn diagram of a number of sets $A_1,\ldots,A_n$ must allocate some territory (with positive area) for any of the possible intersections $\left(A_{j_1} \cap \ldots \cap A_{j_m}\right)\setminus (A_{j_{m+1}}\cup\ldots \cup A_{j_n})$. A stricter requirement could be that one demands that each of these allocated regions is connected: Feel free to discuss this further restriction in your answer.
