Arkivo:Venn0001.svg

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Titulo

DeskriptoVenn0001.svg	Intersection math
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One of 16 Venn diagrams, representing 2-ary Boolean functions like set operations and logical 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 to this Hasse diagram.) In set theory the Venn diagrams represent the set, which is marked in red.	These 15 relations, except the empty one, are minterms and can be the case. The relations in the files below are disjunctions. The red fields of their 4x4 matrices tell, in which of these 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. (The existential quantifications for the red intersections are combined by or. They can be combined by the exclusive or as well.)	Relations like subset 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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	Dato/Horo	Dimensioni	Uzero	Komento
aktuala	22:17, 28 sep. 2024	410 × 299 (3 KB)	Watchduck	Shade of red and thinner lines match other image sets.
	15:10, 16 jul. 2024	400 × 300 (613 bicoki)	Antonsusi	validizing, easier code
	23:14, 1 mar. 2024	384 × 280 (3 KB)	Watchduck	cleaner code and lighter red (overwritten with Pywikibot)
	14:06, 26 jul. 2009	384 × 280 (3 KB)	Watchduck
	14:05, 26 jul. 2009	384 × 280 (3 KB)	Watchduck
	13:24, 26 jan. 2008	615 × 463 (4 KB)	Watchduck	{{Information \|Description= \|Source=eigene arbeit \|Date= \|Author= Tilman Piesk \|Permission= \|other_versions= }}
	15:57, 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= }}
	14:26, 22 jan. 2008	480 × 360 (3 KB)	Watchduck	{{Information \|Description= \|Source= \|Date= \|Author= \|Permission= \|other_versions= }}

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Logikala konjunciono

Uzado en altra Wiki

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Uzado en als.wikipedia.org
- Menge (Mathematik)
- Mengenlehre
Uzado en am.wikipedia.org
- ስብስብ
- የጋራ ስብስብ
Uzado en anp.wikipedia.org
- समुच्चय सिद्धान्त
Uzado en ar.wikipedia.org
Uzado en ast.wikipedia.org
- Interseición de conxuntos
Uzado en az.wikipedia.org
- Çoxluqlar nəzəriyyəsi
Uzado en bar.wikipedia.org
- Grundlogn vo da Mathematik
Uzado en ba.wikipedia.org
- Күмәклек
Uzado en be-tarask.wikipedia.org
- Мноства
Uzado en be.wikipedia.org
- Мноства
Uzado en bg.wikipedia.org
Uzado en bn.wikipedia.org
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Arkivo:Venn0001.svg

Titulo

Operations and relations in set theory and logic

Titoloj

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Titulo

Operations and relations in set theory and logic

Titoloj

Kozi montrata en ca arkivo

montras Esperanto

datena grando Esperanto

2 908 Bicoko

alteco Esperanto

280 Pixelo

larĝeco Esperanto

384 Pixelo

MIME-tipo Esperanto

image/svg+xml

kontrolsumo Esperanto

a85bb40a017725cd08586a1c770f055653854c0b

Historio dil arkivo

Ligilo al imajo

Uzado en altra Wiki

Metadonaji

montras ^Esperanto

datena grando ^Esperanto

alteco ^Esperanto

larĝeco ^Esperanto

MIME-tipo ^Esperanto

kontrolsumo ^Esperanto