Abstract
Let ℓ be a set-system ofr-element subsets on ann-element set,r≧3. It is proved that if |ℓ|>3.5\(\left( {\begin{array}{*{20}c} n \\ {r - 1} \\ \end{array} } \right)\) then ℓ contains four distinct membersA, B, C, D such thatA∪B=C∪D andA∩B=C∩D=0.
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