Does anyone have any thoughts on this? I have been struggling with it and I'm not sure if it's a hard problem, or easy and I'm just not getting it?
For $n=2$ sets (say $A$ and $B$), it's obviously 4:
- The one where $A \cap B = \emptyset$
- The one in which $A \cap B \neq \emptyset$, but neither set is a subset of the other
- The one where $A \subset B$
- The one where $B \subset A$
(I'm assuming $A \neq B$ in all cases.)
For $n \ge2 $, though it seems rather difficult. I can't think of a systematic way to count them. Originally I thought I could look at all distinct pairs and allow each pair to take on one of three values (representing disjoint, intersecting, and subset). But I've already found a case where two different diagrams can have the same representation this way.
Any ideas? Thanks.