Fitxategi:Venn0001.svg

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Jatorrizko fitxategia (SVG fitxategia, nominaldi 384 × 280 pixel, fitxategiaren tamaina: 3 KB)

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Laburpena

Deskribapena

English: 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.

Data

2008ko urtarrilaren 22a

Jatorria

Norberak egina

Egilea

Watchduck

SVG genesis

SVG irudi honen iturburu kodea baliozkoa.

Fitxategi hau (bektore-irudia) hau Inkscape-ekin sortu da . .

Lizentzia

This work 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.

Fitxategiaren historia

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	Data/Ordua	Iruditxoa	Neurriak	Erabiltzailea	Iruzkina
oraingoa	22:05, 23 urtarrila 2025		384 × 280 (3 KB)	wikimediacommons>Watchduck	correct size

Fitxategiaren erabilera

Fitxategi hau darabilte ondorengo 3 orri hauek:

Fitxategi:Venn0001.svg

Laburpena

Operations and relations in set theory and logic

Lizentzia

Irudi-oineko testuak

Fitxategi honetan agertzen diren itemak

honako hau irudikatzen du

data size ^ingelesa

2.908 Byte

altuera

280 pixel

zabalera

384 pixel

media type ^ingelesa

image/svg+xml

checksum ^ingelesa

a85bb40a017725cd08586a1c770f055653854c0b

Fitxategiaren historia

Fitxategiaren erabilera

Nabigazio menua

Fitxategi:Venn0001.svg

Laburpena

Operations and relations in set theory and logic

Lizentzia

Irudi-oineko testuak

Fitxategi honetan agertzen diren itemak

honako hau irudikatzen du

data size ingelesa

2.908 Byte

altuera

280 pixel

zabalera

384 pixel

media type ingelesa

image/svg+xml

checksum ingelesa

a85bb40a017725cd08586a1c770f055653854c0b

Fitxategiaren historia

Fitxategiaren erabilera

Nabigazio menua

Bilatu

data size ^ingelesa

media type ^ingelesa

checksum ^ingelesa