Given N possibly overlapping sets, give formulas that specify, using intersections and complements of the given sets, N disjoint sets with the same union as the original N sets. The sets that result are to be the same as the given sets in the case where the given sets are already disjoint.

(In reply to re: Suggestions from Proposer by Charlie)

By N sets I really mean an N-term sequence (or indexed family) of sets, both for the originals and the disjointified results, and perhaps should have phrased the problem in this more precise way to avoid any misunderstanding. However, I think it is the case that if the original sets are (pairwise) distinct, then the disjointified results will also turn out to be distinct if the solution I have in mind is used. Thus if "N sets" is taken to mean "N distinct sets," the resuting disjointified sets would then also be N sets in that same sense, if the originals were.

Posted by Richard on 2004-04-04 18:44:30