Subject: By George, I think I've got it.

From: Steven Belknap <[email-masked]>
Date: Sun, 5 Mar 2000 22:54:08 -0600

A student at Yale may belong to zero or more clubs. Some clubs are 
final clubs. A final club is defined as "a club such that membership 
in it precludes membership in any other final club".

1. Call a set, s, of clubs preclusive if being a member of any one 
of the clubs in s precludes being a member of any other club in s.

2. Call a set, m, of clubs maximally preclusive if it is preclusive 
and every proper superset of m is not preclusive.

3. There is one and only one nonempty set, m. (We are told that some 
clubs are final clubs. If there were no nonempty sets m, that would 
violate the conditions of the problem. If there were more than one 
set m, than it would not be possible to know which set m contained 
the final clubs, and a definition of final club would be impossible. 
Since the problem contains a definition, albeit a circular one, a 
definition must be possible and there must be only one nonempty set, 
m.)

4. Call a club, c, a final club iff it is a member of m.

QED

co'o mi'e stivn

Steven Belknap, M.D.
Assistant Professor of Clinical Pharmacology and Medicine
University of Illinois College of Medicine at Peoria