Talaksan:Venn0111.svg

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Buod

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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	Araw/Oras	Mga dimensiyon	tagagamit	Kumento
ngayon	23:10, 1 Marso 2024	380 × 280 (351 B)	Watchduck	cleaner code and lighter red (overwritten with Pywikibot)
	21:48, 24 Pebrero 2023	380 × 280 (352 B)	JoKalliauer	recreated, human redable, more symmetric
	22:39, 19 Nobyembre 2022	512 × 373 (491 B)	TSamuel	Careful recompression via SVGOMG & vecta.io/nano, & verified via SVGCheck
	14:10, 26 Hulyo 2009	384 × 280 (3 KB)	Watchduck
	13:29, 26 Enero 2008	615 × 463 (4 KB)	Watchduck	{{Information \|Description= \|Source=eigene arbeit \|Date= \|Author= Tilman Piesk \|Permission= \|other_versions= }}
	16:03, 22 Enero 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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Paggamit sa als.wikipedia.org
- Menge (Mathematik)
- Mengenlehre
Paggamit sa am.wikipedia.org
- ስብስብ
- ውህድ ስብስብ
Paggamit sa anp.wikipedia.org
- समुच्चय सिद्धान्त
Paggamit sa ar.wikipedia.org
Paggamit sa az.wikipedia.org
- Çoxluqlar nəzəriyyəsi
Paggamit sa bar.wikipedia.org
- Grundlogn vo da Mathematik
Paggamit sa ba.wikipedia.org
- Күмәклек
Paggamit sa be-tarask.wikipedia.org
- Мноства
Paggamit sa be.wikipedia.org
- Мноства
Paggamit sa bg.wikipedia.org
Paggamit sa bn.wikipedia.org
- সেট
- ভেন রেখাচিত্র
Paggamit sa bs.wikipedia.org
- Disjunkcija sudova
Paggamit sa ca.wikipedia.org
Paggamit sa ckb.wikipedia.org
- کۆمەڵە (ماتماتیک)
- تیۆریی کۆمەڵە
Paggamit sa cs.wikipedia.org
Paggamit sa cy.wikipedia.org
- Uniad set
Paggamit sa da.wikipedia.org
- Mængde
Paggamit sa de.wikipedia.org
Paggamit sa de.wikibooks.org

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Haba	380
Taas	280

Talaksan:Venn0111.svg

Buod

Operations and relations in set theory and logic

Captions

Items portrayed in this file

depicts ^English

MIME type ^English

image/svg+xml

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Buod

Operations and relations in set theory and logic

Captions

Items portrayed in this file

depicts English

MIME type English

image/svg+xml

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Mga ugnay

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depicts ^English

MIME type ^English