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Problems(1)

S-family over R

Source:

9/15/2010
Let RR be a set of exactly 66 elements. A set FF of subsets of RR is called an SS-family over RR if and only if it satisfies the following three conditions: (i) For no two sets X,YX, Y in FF is X⊆YX \subseteq Y ;
(ii) For any three sets X,Y,ZX, Y,Z in FF, X∪Y∪Z≠R,X \cup Y \cup Z \neq R,
(iii) ⋃X∈FX=R\bigcup_{X \in F} X = R
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