
Accession Number : AD0768892
Title : Venn Diagrams and Independent Families of Sets.
Descriptive Note : Technical rept.,
Corporate Author : WASHINGTON UNIV SEATTLE
Personal Author(s) : Grunbaum,Branko
Report Date : SEP 1973
Pagination or Media Count : 25
Abstract : Motivated by the well known notions from probability and logic, the author says that a family of n simple closed curves (A sub 1),...,(A sub n) in the Euclidean plane is independent provided the intersection (*) (X sub 1)(X sub 2)...(X sub n) is nonempty whenever each set (X sub j) is either the interior or else the exterior of (A sub j). An independent family is a Venn diagram if each intersection (*) is connected. These notions are examined from the point of view of combinatorial geometry and several results are obtained; some of them correct erroneous assertion found in the literature. (Modified author abstract)
Descriptors : (*CONVEX SETS, GRAPHICS), (*GEOMETRY, *COMBINATORIAL ANALYSIS), MATHEMATICAL LOGIC, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE