Datei:Venn0100.svg

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One of 16Venn diagrams,representing 2-aryBoolean functionslikeset operationsandlogical connectives:

Operations and relations in set theory and logic

∅^c

A = A

A^c

\scriptstyle \cup

B^c

true
^{A ↔ A}

A

\scriptstyle \cup

B

A

\scriptstyle \subseteq

B^c

A

\scriptstyle \Leftrightarrow

A

\scriptstyle \supseteq

B^c

A

\scriptstyle \cup

B^c

¬A

\scriptstyle \lor

¬B
^{A → ¬B}

A

\scriptstyle \Delta

B

A

\scriptstyle \lor

B
^{A ← ¬B}

A^c

\scriptstyle \cup

B

A

\scriptstyle \supseteq

B

A

\scriptstyle \Rightarrow

¬B

A = B^c

A

\scriptstyle \Leftarrow

¬B

A

\scriptstyle \subseteq

B

B^c

A

\scriptstyle \lor

¬B
^{A ← B}

A

\scriptstyle \oplus

B
^{A ↔ ¬B}

A^c

¬A

\scriptstyle \lor

B
^{A → B}

B

B =∅

A

\scriptstyle \Leftarrow

B

A =∅^c

A

\scriptstyle \Leftrightarrow

¬B

A =∅

A

\scriptstyle \Rightarrow

B

B =∅^c

¬B

A

\scriptstyle \cap

B^c

A

(A

\scriptstyle \Delta

B)^c

¬A

A^c

\scriptstyle \cap

B

\scriptstyle \Leftrightarrow

false

A

\scriptstyle \Leftrightarrow

true

A = B

A

\scriptstyle \Leftrightarrow

false

B

\scriptstyle \Leftrightarrow

true

A

\scriptstyle \land

¬B

A^c

\scriptstyle \cap

B^c

A

\scriptstyle \leftrightarrow

B

A

\scriptstyle \cap

B

¬A

\scriptstyle \land

B

A

\scriptstyle \Leftrightarrow

B

¬A

\scriptstyle \land

¬B

∅

A

\scriptstyle \land

B

A = A^c

false
^{A ↔ ¬A}

A

\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, aremintermsand can be the case. The relations in the files below aredisjunctions.The red fields of their 4x4 matrices tell, in which ofthesecases 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 quantificationsfor the red intersections are combined byor. They can becombined by theexclusive oras 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.

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	Version vom	Mäß	Benutzer	Kommentar
aktuell	23:18, 28. Sep. 2024	380 × 280(351 Bytes)	Watchduck	Shade of red and thinner lines match other image sets.
	16:23, 16. Jul. 2024	400 × 300(577 Bytes)	Antonsusi	validizing, easier code
	00:09, 2. Mär. 2024	380 × 280(351 Bytes)	Watchduck	cleaner code and lighter red (overwritten withPywikibot)
	21:29, 24. Jul. 2023	380 × 280(352 Bytes)	SVG-image-maker	Redrew with a text editor
	15:08, 26. Jul. 2009	384 × 280(3 KB)	Watchduck
	14:26, 26. Jan. 2008	615 × 463(4 KB)	Watchduck	{{Information \|Description= \|Source=eigene arbeit \|Date= \|Author=Tilman Piesk\|Permission= \|other_versions= }}
	17:00, 22. Jan. 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= }}