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Disjointification (Posted on 2004-04-04) Difficulty: 3 of 5
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.

See The Solution Submitted by Richard    
Rating: 3.1667 (6 votes)

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Suggestions from Proposer | Comment 2 of 12 |
(In reply to thoughts by Charlie)

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
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