This is a file from the Wikimedia Commons

File:Venn0010.svg

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

Original file ‎(SVG file, nominally 384 × 280 pixels, file size: 3 KB)

Summary

One of 16 Venn diagrams, representing 2-ary Boolean functions like set operations and logical connectives:

X or ¬X¬A or ¬BA or ¬B¬A or BA or B¬B¬AA xor BA xnor BAB¬A and ¬BA and ¬B¬A and BA and BX and ¬XLogical connectives Hasse diagram.svg
About this image


Operations and relations in set theory and logic

 
∅c		           
A = A
1111 1111
 
Ac  Bc		 true
A ↔ A		  
A  B		  
A  Bc		 AA
 		  
A  Bc
1110 0111 1110 0111
 
A  Bc		 ¬A  ¬B
A → ¬B		  
A  B		 A  B
A ← ¬B		  
Ac B		  
A B		 A¬B
 		  
A = Bc		 A¬B
 		  
A B
1101 0110 1011 1101 0110 1011
 
Bc		 A  ¬B
A ← B		  
A		 A  B
A ↔ ¬B		  
Ac		 ¬A  B
A → B		  
B		  
B = ∅		 AB
 		  
A = ∅c		 A¬B
 		  
A = ∅		 AB
 		  
B = ∅c
1100 0101 1010 0011 1100 0101 1010 0011
¬B
 		  
A  Bc		 A
 		  
(A  B)c		 ¬A
 		  
Ac  B		 B
 		 Bfalse
 		 Atrue
 		  
A = B		 Afalse
 		 Btrue
 
0100 1001 0010 0100 1001 0010
A  ¬B
 		  
Ac  Bc		 A  B
 		  
A  B		 ¬A  B
 		 AB
 
1000 0001 1000 0001
¬A  ¬B
 		  
∅		 A  B
 		  
A = Ac
0000 0000
false
A ↔ ¬A		 A¬A
 
These sets (statements) have complements (negations).
They are in the opposite position within this matrix. 		These relations are statements, and have negations.
They are shown in a separate matrix in the box below.




PD-icon.svg This work is ineligible for copyright and therefore in the public domain because it consists entirely of information that is common property and contains no original authorship.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current14:07, 26 July 2009Thumbnail for version as of 14:07, 26 July 2009384 × 280 (3 KB)Watchduck
13:25, 26 January 2008Thumbnail for version as of 13:25, 26 January 2008615 × 463 (4 KB)Watchduck{{Information |Description= |Source=eigene arbeit |Date= |Author= Tilman Piesk |Permission= |other_versions= }}
15:58, 22 January 2008Thumbnail for version as of 15:58, 22 January 2008615 × 463 (4 KB)Watchduck{{Information |Description=Venn diagrams (sometimes called Johnston diagrams) concerning propositional calculus and set theory |Source=own work |Date=2008/Jan/22 |Author=Tilman Piesk |Permission=publich domain |other_versions= }}
The following pages on the English Wikipedia use this file (pages on other projects are not listed):

Global file usage

The following other wikis use this file:

Retrieved from "https://en.wikipedia.org/wiki/File:Venn0010.svg"