Movatterモバイル変換

[0]ホーム

Jump to content

File:Venn1010.svg

Page contents not supported in other languages.

From Wikipedia, the free encyclopedia

Size of this PNG preview of this SVG file:380 × 280 pixels.Other resolutions:320 × 236 pixels |640 × 472 pixels |1,024 × 755 pixels |1,280 × 943 pixels |2,560 × 1,886 pixels.

Original file(SVG file, nominally 380 × 280 pixels, file size: 351 bytes)

This is a file from theWikimedia Commons. Information from itsdescription page there is shown below.
Commons is a freely licensed media file repository.You can help.

Summary

One of 16Venn diagrams, representing 2-aryBoolean functions likeset operations and [[w:Logical corect 81 233 166 409¬A or ¬Brect 260 231 349 409A or ¬Brect 393 230 481 409¬A or Brect 574 232 663 408A or Brect 13 436 103 617¬Brect 147 438 235 617¬Arect 279 440 368 616A xor Brect 375 440 464 617A xnor Brect 507 439 595 617Arect 639 438 732 617Brect 79 647 168 826¬A and ¬Brect 260 647 349 826A and ¬Brect 392 646 482 826¬A and Brect 574 646 663 826A and Brect 327 853 417 1035X and ¬Xdesc top-right</imagemap>

Operations and relations in set theory and logic

∅^c

A = A

A^c

\scriptstyle \cup

B^c

true
^{A ↔ A}

\scriptstyle \cup

\scriptstyle \subseteq

B^c

\scriptstyle \Leftrightarrow

\scriptstyle \supseteq

B^c

\scriptstyle \cup

B^c

¬A

\scriptstyle \lor

¬B
^{A → ¬B}

\scriptstyle \Delta

\scriptstyle \lor

B
^{A ← ¬B}

A^c

\scriptstyle \cup

\scriptstyle \supseteq

\scriptstyle \Rightarrow

¬B

A = B^c

\scriptstyle \Leftarrow

¬B

\scriptstyle \subseteq

B^c

\scriptstyle \lor

¬B
^{A ← B}

\scriptstyle \oplus

B
^{A ↔ ¬B}

A^c

¬A

\scriptstyle \lor

B
^{A → B}

B =∅

\scriptstyle \Leftarrow

A =∅^c

\scriptstyle \Leftrightarrow

¬B

A =∅

\scriptstyle \Rightarrow

B =∅^c

¬B

\scriptstyle \cap

B^c

\scriptstyle \Delta

B)^c

¬A

A^c

\scriptstyle \cap

\scriptstyle \Leftrightarrow

false

\scriptstyle \Leftrightarrow

true

A = B

\scriptstyle \Leftrightarrow

false

\scriptstyle \Leftrightarrow

true

\scriptstyle \land

¬B

A^c

\scriptstyle \cap

B^c

\scriptstyle \leftrightarrow

\scriptstyle \cap

¬A

\scriptstyle \land

\scriptstyle \Leftrightarrow

¬A

\scriptstyle \land

¬B

∅

\scriptstyle \land

A = A^c

false
^{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, areminterms and can be the case.
The relations in the files below aredisjunctions. The red fields of their 4x4 matrices tell, in which ofthese 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.
(Theexistential quantifications for the red intersections are combined byor.
They can becombined by theexclusive or as 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.

Public domainPublic domainfalsefalse

This work isineligible forcopyright and therefore in thepublic domain because it consists entirely of information that iscommon property and contains no original authorship.

derivative works

Derivative works of this file: Komplement einer Menge.svg

Captions

English

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

copyright status

public domain

media type

image/svg+xml

data size

351byte

checksum

0c4e108e2ba29d17fbc668be2d03a235fd73345d

determination method or standard:SHA-1

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Dimensions	User	Comment
current	22:20, 28 September 2024	380 × 280(351 bytes)	Watchduck	Shade of red and thinner lines match other image sets.
	15:38, 16 July 2024	400 × 300(518 bytes)	Antonsusi	Valid SVG
	23:09, 1 March 2024	380 × 280(351 bytes)	Watchduck	cleaner code and lighter red (overwritten withPywikibot)
	20:39, 24 July 2023	380 × 280(352 bytes)	SVG-image-maker	Redrew with a text editor
	14:11, 26 July 2009	384 × 280(3 KB)	Watchduck
	13:31, 26 January 2008	615 × 463(4 KB)	Watchduck	{{Information \|Description= \|Source=eigene arbeit \|Date= \|Author=Tilman Piesk \|Permission= \|other_versions= }}
	16:05, 22 January 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= }}