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(3): Suggestions from Proposer
Thank you for the example. An example (as well as a picture) is worth a thousand words, at least for us who are somewhat mentally handicapped. Now I understand what you have been griping about. I should have said "N-term sequence of sets" in place of "N sets," since a common interpretation of "N sets" is "N distinct sets." The empty set, by the way, is disjoint from any set, including the empty set, with the usual definition of "disjoint" being "having no element in common."
Posted by Richard
on 2004-04-04 20:49:44