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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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Solution Solution | Comment 4 of 12 |
If we have sets A, B, C, ... Y, Z, a solution is

A' = A - B - C - ... - Y - Z
B' = B - C - ... - Y - Z
C' = C - ... - Y - Z
...
Y' = Y - Z
Z' = Z

If you want to use just intersections and complements, apply the fact that P-Q = P intersection (complement of Q).

  Posted by Federico Kereki on 2004-04-04 15:30:49
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