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 Suggestions from Proposer by Richard)

Given the notation provided by Richard, and the lack of need to assure that the sets are distinct or non-null, then given sets A, B, C,  etc., the required sets are A, BA', CA'B', DA'B'C', EA'B'C'D', etc.

The problem is that several of these may be empty and therefore identical, and therefore we don't actually have N sets, but some smaller number, even though different names or formulae might apply to the same set.

Posted by Charlie on 2004-04-04 13:25:50