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 thoughts
Charlie and any others who work on this one:
It is easiest to just use juxtaposition to indicate intersection and a prime to indicate complement so that the intersection of A with the complement of B would be denoted by AB'.
The problem does not say that the given N sets are distinct -- here we are dealing with a given finite sequence of sets, some of which can be the empty set, and you are to produce a sequence, of the same length, and that is guaranteed to be made up of sets no two of which have a nonempty intersection.
I hope this satisfies all the those who have "technical" concerns. This is not intended to be a trick problem where technicalities are important.
Posted by Richard
on 2004-04-04 13:15:03