File:Venn1001.svg

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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 ¬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

 
∅c
          
A = A
1111 1111
 
Ac  Bc
true
A ↔ A
 
A  ∪ {\displaystyle \scriptstyle \cup }  B
 
A  ⊆ {\displaystyle \scriptstyle \subseteq }  Bc
AA
 
 
 Bc
1110 0111 1110 0111
 
 Bc
¬A  ∨ {\displaystyle \scriptstyle \lor }  ¬B
A → ¬B
 
A  Δ {\displaystyle \scriptstyle \Delta }  B
A  ∨ {\displaystyle \scriptstyle \lor }  B
A ← ¬B
 
Ac B
 
A B
A¬B
 
 
A = Bc
A¬B
 
 
A ⊆ {\displaystyle \scriptstyle \subseteq } B
1101 0110 1011 1101 0110 1011
 
Bc
A  ∨ {\displaystyle \scriptstyle \lor }  ¬B
A ← B
 
A
A  ⊕ {\displaystyle \scriptstyle \oplus }  B
A ↔ ¬B
 
Ac
¬A  ∨ {\displaystyle \scriptstyle \lor }  B
A → B
 
B
 
B =
AB
 
 
A = c
A¬B
 
 
A =
AB
 
 
B = c
1100 0101 1010 0011 1100 0101 1010 0011
¬B
 
 
 Bc
A
 
 
(A  B)c
¬A
 
 
Ac  B
B
 
Bfalse
 
Atrue
 
 
A = B
Afalse
 
Btrue
 
0100 1001 0010 0100 1001 0010
A  ∧ {\displaystyle \scriptstyle \land }  ¬B
 
 
Ac  Bc
A  ↔ {\displaystyle \scriptstyle \leftrightarrow }  B
 
 
A  ∩ {\displaystyle \scriptstyle \cap }  B
¬A  ∧ {\displaystyle \scriptstyle \land }  B
 
AB
 
1000 0001 1000 0001
¬A  ∧ {\displaystyle \scriptstyle \land }  ¬B
 
 
A  ∧ {\displaystyle \scriptstyle \land }  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 separate 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

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

Date/Time Thumbnail Dimensions User Comment
current 14:11, 26 July 2009 Thumbnail for version as of 14:11, 26 July 2009 384 × 280 (3 KB) Watchduck
13:31, 26 January 2008 Thumbnail for version as of 13:31, 26 January 2008 615 × 463 (4 KB) Watchduck {{Information |Description= |Source=eigene arbeit |Date= |Author= Tilman Piesk |Permission= |other_versions= }}
16:04, 22 January 2008 Thumbnail for version as of 16:04, 22 January 2008 615 × 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= }}

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