High Quality Content by WIKIPEDIA articles! In combinatorial mathematics, the union-closed sets conjecture is an elementary problem, posed by Peter Frankl in 1979 and still open as of 2008[update]. A family of sets is said to be union-closed if the union of any two sets from the family remains in the family. The conjecture states that for any finite union-closed family of finite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the sets in the family.

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