IMO 1979 LL ROM57

Let M be a set, and A, B, C given subsets of M. Find a

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IMO 1979 LL ROM57

Origin: ROM

Problem

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 \subsetM for which (X \cupA) \ (X \capB) = C. Describe all such sets X.