ಚಿತ್ರ:Venn0111.svg

Size of this PNG preview of this SVG file: ೩೮೦ × ೨೮೦ ಪಿಕ್ಸೆಲ್‌ಗಳು. ಇತರ ರೆಸಲ್ಯೂಶನ್ಗಳು: ೩೨೦ × ೨೩೬ ಪಿಕ್ಸೆಲ್‌ಗಳು | ೬೪೦ × ೪೭೨ ಪಿಕ್ಸೆಲ್‌ಗಳು | ೧,೦೨೪ × ೭೫೫ ಪಿಕ್ಸೆಲ್‌ಗಳು | ೧,೨೮೦ × ೯೪೩ ಪಿಕ್ಸೆಲ್‌ಗಳು | ೨,೫೬೦ × ೧,೮೮೬ ಪಿಕ್ಸೆಲ್‌ಗಳು.

ಮೂಲ ಕಡತ (SVG ಫೈಲು, ಸುಮಾರಾಗಿ ೩೮೦ × ೨೮೦ ಚಿತ್ರಬಿಂದುಗಳು, ಫೈಲಿನ ಗಾತ್ರ: ೩೫೧ byte)

ಸಾರಾಂಶ

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.

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.

ಕಡತದ ಇತಿಹಾಸ

ದಿನ/ಕಾಲ ಒತ್ತಿದರೆ ಆ ಸಮಯದಲ್ಲಿ ಈ ಕಡತದ ವಸ್ತುಸ್ಥಿತಿ ತೋರುತ್ತದೆ.

	ದಿನ/ಕಾಲ	ಆಯಾಮಗಳು	ಬಳಕೆದಾರ	ಟಿಪ್ಪಣಿ
ಪ್ರಸಕ್ತ	೦೩:೪೯, ೨೯ ಸೆಪ್ಟೆಂಬರ್ ೨೦೨೪	೩೮೦ × ೨೮೦ (೩೫೧ byte)	Watchduck	Shade of red and thinner lines match other image sets.
	೨೧:೦೨, ೧೬ ಜುಲೈ ೨೦೨೪	೪೦೦ × ೩೦೦ (೬೧೪ byte)	Antonsusi	Valid SVG
	೦೪:೪೦, ೨ ಮಾರ್ಚ್ ೨೦೨೪	೩೮೦ × ೨೮೦ (೩೫೧ byte)	Watchduck	cleaner code and lighter red (overwritten with Pywikibot)
	೦೩:೧೮, ೨೫ ಫೆಬ್ರವರಿ ೨೦೨೩	೩೮೦ × ೨೮೦ (೩೫೨ byte)	JoKalliauer	recreated, human redable, more symmetric
	೦೪:೦೯, ೨೦ ನವೆಂಬರ್ ೨೦೨೨	೫೧೨ × ೩೭೩ (೪೯೧ byte)	TSamuel	Careful recompression via SVGOMG & vecta.io/nano, & verified via SVGCheck
	೧೯:೪೦, ೨೬ ಜುಲೈ ೨೦೦೯	೩೮೪ × ೨೮೦ (೩ KB)	Watchduck
	೧೮:೫೯, ೨೬ ಜನವರಿ ೨೦೦೮	೬೧೫ × ೪೬೩ (೪ KB)	Watchduck	{{Information \|Description= \|Source=eigene arbeit \|Date= \|Author= Tilman Piesk \|Permission= \|other_versions= }}
	೨೧:೩೩, ೨೨ ಜನವರಿ ೨೦೦೮	೬೧೫ × ೪೬೩ (೪ 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= }}