फाईल:Venn0111.svg

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सारांश

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.

यह चित्र कॉपीराइट के लिए अयोग्य है और इसलिए सार्वजनिक डोमेन में है क्योंकि इसमें सिर्फ ऐसी जानकारी है जो साधारण संपत्ति है और यह मौलिक रचना से मुक्त है।

फाइल केरौ इतिहास

संचिका पुरानौ समय मँ कैन्हौ दिखै छेलै इ जानै लेली वांछित दिनांक/समय प चाँपौ।

	दिनांक/समय	आयाम	सदस्य	टिप्पणी
वर्तमान	०४:४०, २ मार्च २०२४	३८० × २८० (३५१ B)	Watchduck	cleaner code and lighter red (overwritten with Pywikibot)
	०३:१८, २५ फरवरी २०२३	३८० × २८० (३५२ B)	JoKalliauer	recreated, human redable, more symmetric
	०४:०९, २० नवंबर २०२२	५१२ × ३७३ (४९१ B)	TSamuel	Careful recompression via SVGOMG & vecta.io/nano, & verified via SVGCheck
	१९:४०, २६ जुलाई २००९	३८४ × २८० (३ KB)	Watchduck
	१८:५९, २६ जनवरी २००८	६१५ × ४६३ (४ KB)	Watchduck	{{Information \|Description= \|Source=eigene arbeit \|Date= \|Author= Tilman Piesk \|Permission= \|other_versions= }}
	२१:३३, २२ जनवरी २००८	६१५ × ४६३ (४ 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= }}