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File:Venn and Euler diagrams of 3-ary Boolean relations.svg

Original file(SVG file, nominally 2,253 × 2,299 pixels, file size: 299 KB)

Summary

Description

Venn diagrams (top) and Euler diagrams (bottom) of relations corresponding to 3-ary Boolean functions
Areas marked black contain no elements. Euler diagrams avoid showing empty areas, but this is not always possible.


See also: v:User:Watchduck/Logic#3-ary relations


Each function belongs to one of Sloane'sA000616(3) = 22 big equivalence classes (becs).
Relations from complementary becs are ordered symmetrically to the vertical middle axis of the image - except in rectangle 4: All relations with 4 white areas are from self complementary becs.


Each one of the 256 possible relations can be expressed by one of these Euler diagrams by permuting and negating the arguments A, B, C.
E.g. Relation 0010 0111.svg can be expressed by Relation 0010 0111 (Euler diagram).svg.


The beige numbers denote the number of white areas in the diagrams in the corresponding beige rectangle.
(That is the number of ones in the corresponding Boolean functions.)

The number of relations in each beige rectangle is Sloane'sA039754(3; 0..8) = (1, 1, 3, 3, 6, 3, 3, 1, 1).
Source Own work
Author Watchduck.svg Watchduck (a.k.a. Tilman Piesk)
Other versions
With dual graphs of the Euler diagrams

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GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
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Date/TimeThumbnailDimensionsUserComment
current19:58, 5 March 2016Thumbnail for version as of 19:58, 5 March 20162,253 × 2,299 (299 KB)Watchducklayout
10:41, 14 August 2014Thumbnail for version as of 10:41, 14 August 20142,253 × 2,299 (316 KB)Watchduckchange in box 4
20:38, 1 August 2014Thumbnail for version as of 20:38, 1 August 20142,253 × 2,299 (317 KB)Watchduck{{Information |Description ={{en|1=upload forms suck}} |Source ={{own}} |Author ={{Mate2code}} |Date = |Permission = |other_versions = }}
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