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File:Venn0001.svg

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Summary[edit]

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

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


Operations and relations in set theory and logic[edit]

 
∅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 or statements have complements
or negations. They are shown inside this matrix.		 These relations are statements, and have negations.
They are shown in a seperate matrix in the box below.




PD-icon.svg This file 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

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Date/TimeThumbnailDimensionsUserComment
current14:06, 26 July 2009Thumbnail for version as of 14:06, 26 July 2009384 × 280 (3 KB)Watchduck
14:05, 26 July 2009Thumbnail for version as of 14:05, 26 July 2009384 × 280 (3 KB)Watchduck
13:24, 26 January 2008Thumbnail for version as of 13:24, 26 January 2008615 × 463 (4 KB)Watchduck{{Information |Description= |Source=eigene arbeit |Date= |Author= Tilman Piesk |Permission= |other_versions= }}
15:57, 22 January 2008Thumbnail for version as of 15:57, 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= }}
14:26, 22 January 2008Thumbnail for version as of 14:26, 22 January 2008480 × 360 (3 KB)Watchduck{{Information |Description= |Source= |Date= |Author= |Permission= |other_versions= }}

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Width 307.28000pt
Height 223.89000pt
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