On Property of Families of Sets

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Abstract
A family of sets is said to have property if there exists a set B such that B ∩ F ≠ Ø and B ⊅ F for every F ∊ . Such a B will be called suitable with respect to F. It is known (see [3]) that for each positive integer n there exists a family of sets satisfying the following conditions: (a)|F| = n for each F ∊ (b)|F ∩ G| ≤ for F, G ∊ F ≠ G (c) does not have property

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