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Necessary and sufficient condition for the existence of a se

Source: ILL 1979 - Problem 57.

June 5, 2011

combinatorics unsolvedcombinatorics

Problem Statement

Let

M

be a set and

A,B,C

given subsets of

M

. Find a necessary and sufficient condition for the existence of a set

X\subset M

for which

(X\cup A)\backslash(X\cap B)=C

. Describe all such sets.