Subset Serve as Graph Vertices

    Wafiq Hibi

    Abstract

    In [7], the following claim was given: If S is a set of 10 elements, and if we choose a collection T of more than (■ (10@4)) subsets of S, when all A sub-sets from this collection exist,

     3≤|A|≤4, Then there are two subsets A_1 and A_2 in T so that A_1⊆A_2.

    I will extend this example, to any general cardinality of a given set.

    Additionally, we will even prove that the two sub-sets A_1 and A_2 fulfill that A_1⊂A_2.

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