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 Solution? Too simple?
The union of two sets is the same as the complement of the intersection of their complements (DeMorgan's law). And yes, the last condition rules out just taking the union as the first set and using all empty sets for the rest -- your example motivated adding that last condition, in fact.
As a hint, try just two sets to start.
Posted by Richard
on 2004-04-05 13:24:58