Fasciculus:Venn0001.svg

Size of this PNG preview of this SVG file: 384 × 280 elementa imaginalia. Aliae mensurae: 320 × 233 elementa imaginalia | 640 × 467 elementa imaginalia | 1 024 × 747 elementa imaginalia | 1 280 × 933 elementa imaginalia | 2 560 × 1 867 elementa imaginalia.

Sua resolutio (fasciculus SVG, nominale 384 × 280 elementa imaginalia, magnitudo fasciculi: 3 chiliocteti)

Hic fasciculus apud Vicimedia Communia iacet; in aliis inceptis adhiberi potest. Contenta paginae descriptionis fasciculi subter monstrantur.

Summarium

Descriptio

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.

Datum

22 Ianuarius 2008

Fons

Opus proprium

Auctor

Watchduck

SVG genesis

The SVG code is valid.

This diagram was created with Inkscape.

Potestas usoris

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.

Historia fasciculi

Presso die vel tempore fasciculum videbis, sicut tunc temporis apparuit.

	Dies/Tempus	Minutio	Dimensiones	Usor	Sententia
recentissima	22:05, 23 Ianuarii 2025		384 × 280 (3 chiliocteti)	wikimediacommons>Watchduck	correct size

Nexus ad fasciculum

Ad hunc fasciculum nectit:

Copia

Fasciculus:Venn0001.svg

Summarium

Operations and relations in set theory and logic

Potestas usoris

Captions

Items portrayed in this file

depicts ^Anglica

data size ^Anglica

2 908 byte

altitudo

280 Pixel

latitudo

384 Pixel

media type ^Anglica

image/svg+xml

checksum ^Anglica

a85bb40a017725cd08586a1c770f055653854c0b

Historia fasciculi

Nexus ad fasciculum

Tabula navigationis

Fasciculus:Venn0001.svg

Summarium

Operations and relations in set theory and logic

Potestas usoris

Captions

Items portrayed in this file

depicts Anglica

data size Anglica

2 908 byte

altitudo

280 Pixel

latitudo

384 Pixel

media type Anglica

image/svg+xml

checksum Anglica

a85bb40a017725cd08586a1c770f055653854c0b

Historia fasciculi

Nexus ad fasciculum

Tabula navigationis

Quaerere

depicts ^Anglica

data size ^Anglica

media type ^Anglica

checksum ^Anglica