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  • 21 Aug, 2019

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File:Venn0001.svg
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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 ¬X


Operations and relations in set theory and logic

 
∅		           
A = A
1111 1111
 
A  B		 true
  
A  B		  
A  B		 AA
  
A  B
1110 0111 1110 0111
 
A  B		 ¬A  ¬B
  
A  B		 A  B
  
A B		  
A B		 A¬B
  
A = B		 A¬B
  
A B
1101 0110 1011 1101 0110 1011
 
B		 A  ¬B
  
A		 A  B
  
A		 ¬A  B
  
B		  
B = ∅		 AB
  
A = ∅		 A¬B
  
A = ∅		 AB
  
B = ∅
1100 0101 1010 0011 1100 0101 1010 0011
¬B
  
A  B		 A
  
(A  B)		 ¬A
  
A  B		 B
 Bfalse
 Atrue
  
A = B		 Afalse
 Btrue
0100 1001 0010 0100 1001 0010
A  ¬B
  
A  B		 A  B
  
A  B		 ¬A  B
 AB
1000 0001 1000 0001
¬A  ¬B
  
∅		 A  B
  
A = A
0000 0000
false
 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.



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.

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current23:14, 1 March 2024Thumbnail for version as of 23:14, 1 March 2024384 × 280 (3 KB)Watchduckcleaner code and lighter red (overwritten with Pywikibot)
14:06, 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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