ملف:Venn0010.svg

حجم معاينة PNG لذلك الملف ذي الامتداد SVG: 380 × 280 بكسل. الأبعاد الأخرى: 320 × 236 بكسل | 640 × 472 بكسل | 1٬024 × 755 بكسل | 1٬280 × 943 بكسل | 2٬560 × 1٬886 بكسل.

الملف الأصلي (ملف SVG، أبعاده 380 × 280 بكسل، حجم الملف: 351 بايت)

هذا ملف من ويكيميديا كومنز. معلومات من صفحة وصفه مبينة في الأسفل. كومنز مستودع ملفات ميديا ذو رخصة حرة.

ملخص

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.

ليسَ لهذه الصُّورة حقوق تأليفٍ ونشرٍ لأنَّها مُكوَّنة بالكامِل من معلومات عامَّة ولا تحتوي على عملٍ أَصيلٍ. ولذلك فهي في النطاق العامّّ .

تاريخ الملف

اضغط على زمن/تاريخ لرؤية الملف كما بدا في هذا الزمن.

	زمن/تاريخ	الأبعاد	مستخدم	تعليق
حالي	22:18، 28 سبتمبر 2024	380 × 280 (351 بايت)	Watchduck	Shade of red and thinner lines match other image sets.
	15:17، 16 يوليو 2024	400 × 300 (579 بايت)	Antonsusi	validizing, easier code
	23:13، 1 مارس 2024	380 × 280 (351 بايت)	Watchduck	cleaner code and lighter red (overwritten with Pywikibot)
	20:44، 24 يوليو 2023	380 × 280 (352 بايت)	SVG-image-maker	Recoded manually by use of text editor
	14:07، 26 يوليو 2009	384 × 280 (3 كيلوبايت)	Watchduck
	13:25، 26 يناير 2008	615 × 463 (4 كيلوبايت)	Watchduck	{{Information \|Description= \|Source=eigene arbeit \|Date= \|Author= Tilman Piesk \|Permission= \|other_versions= }}
	15:58، 22 يناير 2008	615 × 463 (4 كيلوبايت)	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= }}