File:Venn1011.svg

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Venn1011.svg‎ (SVG file, nominally 384 × 280 pixels, file size: 3 KB)

[edit] Summary

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


[edit] Operations and relations in set theory and logic

 
∅c		           
A = A
1111 1111
 
Ac \cup Bc		 true
A ↔ A		  
A \cup B		  
A \subseteq Bc		 A\LeftrightarrowA
 		  
A \supseteq Bc
1110 0111 1110 0111
 
A \cup Bc		 ¬A \or ¬B
A → ¬B		  
A \Delta B		 A \or B
A ← ¬B		  
Ac \cup B		  
A \supseteq B		 A\Rightarrow¬B
 		  
A = Bc		 A\Leftarrow¬B
 		  
A \subseteq B
1101 0110 1011 1101 0110 1011
 
Bc		 A \or ¬B
A ← B		  
A		 A \oplus B
A ↔ ¬B		  
Ac		 ¬A \or B
A → B		  
B		  
B = ∅		 A\LeftarrowB
 		  
A = ∅c		 A\Leftrightarrow¬B
 		  
A = ∅		 A\RightarrowB
 		  
B = ∅c
1100 0101 1010 0011 1100 0101 1010 0011
¬B
 		  
A \cap Bc		 A
 		  
(A \Delta B)c		 ¬A
 		  
Ac \cap B		 B
 		 B\Leftrightarrowfalse
 		 A\Leftrightarrowtrue
 		  
A = B		 A\Leftrightarrowfalse
 		 B\Leftrightarrowtrue
 
0100 1001 0010 0100 1001 0010
A \and ¬B
 		  
Ac \cap Bc		 A \leftrightarrow B
 		  
A \cap B		 ¬A \and B
 		 A\LeftrightarrowB
 
1000 0001 1000 0001
¬A \and ¬B
 		  
∅		 A \and B
 		  
A = Ac
0000 0000
false
A ↔ ¬A		 A\Leftrightarrow¬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.

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File history

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

Date/TimeThumbnailDimensionsUserComment
current14:12, 26 July 2009Thumbnail for version as of 14:12, 26 July 2009384 × 280 (3 KB)Lipedia ( )
13:32, 26 January 2008Thumbnail for version as of 13:32, 26 January 2008615 × 463 (4 KB)Lipedia ({{Information |Description= |Source=eigene arbeit |Date= |Author= Tilman Piesk |Permission= |other_versions= }} )
16:06, 22 January 2008Thumbnail for version as of 16:06, 22 January 2008615 × 463 (4 KB)Lipedia ({{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= }} )
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Width 384
Height 280
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