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File:Venn1111.svg

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File:Venn1111.svg
Size of this PNG preview of this SVG file:380 × 280 pixels.Other resolutions:320 × 236 pixels |640 × 472 pixels |1,024 × 755 pixels |1,280 × 943 pixels |2,560 × 1,886 pixels.

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Summary

One of 16Venn diagrams, representing 2-aryBoolean functions likeset operations andlogical connectives:


 
∅c		         
A = A
11111111
 
Ac ∪{\displaystyle \scriptstyle \cup } Bc		true
A ↔ A		 
A ∪{\displaystyle \scriptstyle \cup } B		 
A ⊆{\displaystyle \scriptstyle \subseteq } Bc		A⇔{\displaystyle \scriptstyle \Leftrightarrow }A
 		 
A ⊇{\displaystyle \scriptstyle \supseteq } Bc
1110011111100111
 
A ∪{\displaystyle \scriptstyle \cup } Bc		¬A ∨{\displaystyle \scriptstyle \lor } ¬B
A → ¬B		 
A Δ{\displaystyle \scriptstyle \Delta } B		A ∨{\displaystyle \scriptstyle \lor } B
A ← ¬B		 
Ac∪{\displaystyle \scriptstyle \cup } B		 
A⊇{\displaystyle \scriptstyle \supseteq } B		A⇒{\displaystyle \scriptstyle \Rightarrow }¬B
 		 
A = Bc		A⇐{\displaystyle \scriptstyle \Leftarrow }¬B
 		 
A⊆{\displaystyle \scriptstyle \subseteq } B
110101101011110101101011
 
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 =∅		A⇐{\displaystyle \scriptstyle \Leftarrow }B
 		 
A =∅c		A⇔{\displaystyle \scriptstyle \Leftrightarrow }¬B
 		 
A =∅		A⇒{\displaystyle \scriptstyle \Rightarrow }B
 		 
B =∅c
11000101101000111100010110100011
¬B
 		 
A ∩{\displaystyle \scriptstyle \cap } Bc		A
 		 
(A Δ{\displaystyle \scriptstyle \Delta } B)c		¬A
 		 
Ac ∩{\displaystyle \scriptstyle \cap } B		B
 		B⇔{\displaystyle \scriptstyle \Leftrightarrow }false
 		A⇔{\displaystyle \scriptstyle \Leftrightarrow }true
 		 
A = B		A⇔{\displaystyle \scriptstyle \Leftrightarrow }false
 		B⇔{\displaystyle \scriptstyle \Leftrightarrow }true
 
010010010010010010010010
A ∧{\displaystyle \scriptstyle \land } ¬B
 		 
Ac ∩{\displaystyle \scriptstyle \cap } Bc		A ↔{\displaystyle \scriptstyle \leftrightarrow } B
 		 
A ∩{\displaystyle \scriptstyle \cap } B		¬A ∧{\displaystyle \scriptstyle \land } B
 		A⇔{\displaystyle \scriptstyle \Leftrightarrow }B
 
1000000110000001
¬A ∧{\displaystyle \scriptstyle \land } ¬B
 		 
∅		A ∧{\displaystyle \scriptstyle \land } B
 		 
A = Ac
00000000
false
A ↔ ¬A		A⇔{\displaystyle \scriptstyle \Leftrightarrow }¬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.
more relations

The operations, arranged in the same matrix as above.
The 2x2 matrices show the same information like the Venn diagrams.
(This matrix is similar tothis Hasse diagram.) 
 
In set theory the Venn diagrams represent the set,
which is marked in red.
 

These 15 relations, except the empty one, areminterms and can be the case.
The relations in the files below aredisjunctions. The red fields of their 4x4 matrices tell, in which ofthese cases the relation is true.
(Inherently only conjunctions can be the case. Disjunctions are true in several cases.)
In set theory the Venn diagrams tell,
that there is an element in every red,
and there is no element in any black intersection.

Negations of the relations in the matrix on the right.
In the Venn diagrams the negation exchanges black and red.
 
In set theory the Venn diagrams tell,
that there is an element in one of the red intersections.
(Theexistential quantifications for the red intersections are combined byor.
They can becombined by theexclusive or as well.)

Relations likesubset and implication,
arranged in the same kind of matrix as above.
 
In set theory the Venn diagrams tell,
that there is no element in any black intersection.
 
 



Public domainPublic domainfalsefalse
This work isineligible forcopyright and therefore in thepublic domain because it consists entirely of information that iscommon property and contains no original authorship.

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File history

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Date/TimeThumbnailDimensionsUserComment
current22:19, 28 September 2024Thumbnail for version as of 22:19, 28 September 2024380 × 280(351 bytes)WatchduckShade of red and thinner lines match other image sets.
15:50, 16 July 2024Thumbnail for version as of 15:50, 16 July 2024400 × 300(515 bytes)AntonsusiValid SVG
23:11, 1 March 2024Thumbnail for version as of 23:11, 1 March 2024380 × 280(351 bytes)Watchduckcleaner code and lighter red (overwritten withPywikibot)
20:06, 24 July 2023Thumbnail for version as of 20:06, 24 July 2023380 × 280(352 bytes)SVG-image-makerRecoded manually using the Venn0111 file
21:19, 6 May 2010Thumbnail for version as of 21:19, 6 May 2010384 × 280(3 KB)Watchduckre-upload, hope the borderless version will be shown now
14:14, 26 July 2009Thumbnail for version as of 14:14, 26 July 2009384 × 280(3 KB)Watchduck
13:37, 26 January 2008Thumbnail for version as of 13:37, 26 January 2008615 × 463(4 KB)Watchduck{{Information |Description= |Source=eigene arbeit |Date= |Author=Tilman Piesk |Permission= |other_versions= }}
16:09, 22 January 2008Thumbnail for version as of 16:09, 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= }}

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Height280
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