File:Venn1000.svg

此SVG文件的PNG预览的大小：380 × 280像素。其他分辨率：320 × 236像素 | 640 × 472像素 | 1,024 × 755像素 | 1,280 × 943像素 | 2,560 × 1,886像素。

原始文件（SVG文件，尺寸为380 × 280像素，文件大小：351字节）

本文件并非来自中文维基百科，而是来自维基共享资源。请参阅维基共享资源上的详细描述、讨论页、页面历史、日志。

维基共享资源是一个储存自由版权作品的项目。您可以向此项目作出贡献。

摘要

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.

此作品不具有版权，属于公有领域，因为其所包含之内容均为公共财产且没有明确的原始作者信息。

文件历史

点击某个日期/时间查看对应时刻的文件。

	日期/时间	大小	用户	备注
当前	2024年9月28日 (六) 22:19	380 × 280（351字节）	Watchduck	Shade of red and thinner lines match other image sets.
	2024年7月16日 (二) 15:35	400 × 300（614字节）	Antonsusi	Valid SVG
	2024年3月1日 (五) 23:10	380 × 280（351字节）	Watchduck	cleaner code and lighter red (overwritten with Pywikibot)
	2023年7月24日 (一) 20:33	380 × 280（352字节）	SVG-image-maker	Redrew with a text editor
	2009年7月26日 (日) 14:10	384 × 280（3 KB）	Watchduck
	2008年1月26日 (六) 13:30	615 × 463（4 KB）	Watchduck	{{Information \|Description= \|Source=eigene arbeit \|Date= \|Author= Tilman Piesk \|Permission= \|other_versions= }}
	2008年1月22日 (二) 16:04	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= }}