File:Monotone Boolean functions 0,1,2,3.svg

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Summary

Description

The free distributive lattices of monotonic Boolean functions on up to three variables

The Boolean functions are represented by their Hasse diagrams. (Which are dual to Venn diagrams, as can be seen here.)

A Boolean function is monotonic, when in it's Hasse Diagram there is no 1 (red vertex) connected to a higher 0 (white vertex).

To avoid confusion:
There are four big Hasse diagrams with gray vertices in this file, and they represent lattices of monotone Boolean functions.
In the gray vertices are also Hasse diagrams, and they represent the Boolean functions.
In the vertices of the leftmost Hasse diagram are degenerate Hasse diagrams with only one vertex.

The description of the rightmost Hasse diagram can be included as imagemap:

contradictionA and B and CA and BA and CB and C(A and B) or (A and C)(A and B) or (B and C)(A and C) or (B and C)ABC(A or B) and (A or C) and (B or C) <====> (A and B) or (A and C) or (B and C)(A or B) and (A or C)(A or B) and (B or C)(A or C) and (B or C)A or BA or CB or CA or B or Ctautology
Lattices of monotonic Boolean functions (move mouse over right diagram to see description)

The imagemap links to files, where several Boolean functions are shown.
The monotone function is always in the top right position.

This SVG was created with Inkscape.
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Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
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Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
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Date/TimeThumbnailDimensionsUserComment
current14:55, 19 January 2011Thumbnail for version as of 14:55, 19 January 2011814 × 675 (536 KB)Watchduck== Summary == {{Information |Description={{en|1=The free distributive lattices of monotonic Boolean functions on up to three variables. The Boolean functions are represented b

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