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One of 16 Venn diagrams, representing 2-ary Boolean functions like set operations and logical connectives:
Error: Must specify an image in the first line.
Operations and relations in set theory and logic
∅c
A = A
Ac Bc
true A ↔ A
A B
A Bc
AA
A Bc
A Bc
¬A ¬B A → ¬B
A B
A B A ← ¬B
Ac B
A B
A¬B
A = Bc
A¬B
A B
Bc
A ¬B A ← B
A
A B A ↔ ¬B
Ac
¬A B A → B
B
B = ∅
AB
A = ∅c
A¬B
A = ∅
AB
B = ∅c
¬B
A Bc
A
(A B)c
¬A
Ac B
B
Bfalse
Atrue
A = B
Afalse
Btrue
A ¬B
Ac Bc
A B
A B
¬A B
AB
¬A ¬B
∅
A B
A = Ac
false A ↔ ¬A
A¬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.
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{{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= }}
Bu faylda fotoaparat və ya skanerlə əlavə olunmuş məlumatlar var. Əgər fayl sonradan redaktə olunubsa, bəzi parametrlər bu şəkildə göstərilənlərdən fərqli ola bilər.
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Mart 14, 2023
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Fayl Faylin tarixcesi Fayl kecidleri Faylin qlobal istifadesi MetamelumatlarBu SVG faylin PNG formatindaki bu gorunusunun olcusu 380 280 piksel Diger olculer 320 236 piksel 640 472 piksel 1 024 755 piksel 1 280 943 piksel 2 560 1 886 piksel Faylin orijinali 8206 SVG fayli nominal olaraq 380 280 piksel faylin olcusu 352 bayt Bu fayl Vikimedia Commons dadirve diger layihelerde istifade edile biler Faylin tesvir sehifesine get Xulase One of 16 Venn diagrams representing 2 ary Boolean functions like set operations and logical connectives Error Must specify an image in the first line Operations and relations in set theory and logic nbsp c nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp A A nbsp Ac nbsp displaystyle scriptstyle cup nbsp Bc trueA A nbsp A nbsp displaystyle scriptstyle cup nbsp B nbsp A nbsp displaystyle scriptstyle subseteq nbsp Bc A displaystyle scriptstyle Leftrightarrow A nbsp nbsp A nbsp displaystyle scriptstyle supseteq nbsp Bc nbsp A nbsp displaystyle scriptstyle cup nbsp Bc A nbsp displaystyle scriptstyle lor nbsp BA B nbsp A nbsp D displaystyle scriptstyle Delta nbsp B A nbsp displaystyle scriptstyle lor nbsp BA B nbsp Ac displaystyle scriptstyle cup B nbsp A displaystyle scriptstyle supseteq B A displaystyle scriptstyle Rightarrow B nbsp nbsp A nbsp nbsp Bc A displaystyle scriptstyle Leftarrow B nbsp nbsp A displaystyle scriptstyle subseteq B nbsp Bc A nbsp displaystyle scriptstyle lor nbsp BA B nbsp A A nbsp displaystyle scriptstyle oplus nbsp BA B nbsp Ac A nbsp displaystyle scriptstyle lor nbsp BA B nbsp B nbsp B A displaystyle scriptstyle Leftarrow B nbsp nbsp A c A displaystyle scriptstyle Leftrightarrow B nbsp nbsp A A displaystyle scriptstyle Rightarrow B nbsp nbsp B c B nbsp nbsp A nbsp displaystyle scriptstyle cap nbsp Bc A nbsp nbsp A nbsp D displaystyle scriptstyle Delta nbsp B c A nbsp nbsp Ac nbsp displaystyle scriptstyle cap nbsp B B nbsp B displaystyle scriptstyle Leftrightarrow false nbsp A displaystyle scriptstyle Leftrightarrow true nbsp nbsp A B A displaystyle scriptstyle Leftrightarrow false nbsp B displaystyle scriptstyle Leftrightarrow true nbsp A nbsp displaystyle scriptstyle land nbsp B nbsp nbsp Ac nbsp displaystyle scriptstyle cap nbsp Bc A nbsp displaystyle scriptstyle leftrightarrow nbsp B nbsp nbsp A nbsp displaystyle scriptstyle cap nbsp B A nbsp displaystyle scriptstyle land nbsp B nbsp A displaystyle scriptstyle Leftrightarrow B nbsp A nbsp displaystyle scriptstyle land nbsp B nbsp nbsp A nbsp displaystyle scriptstyle land nbsp B nbsp nbsp A Ac falseA A A displaystyle scriptstyle Leftrightarrow A nbsp 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 nbsp nbsp In set theory the Venn diagrams represent the set which is marked in red nbsp 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 nbsp 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 nbsp In set theory the Venn diagrams tell that there is no element in any black intersection nbsp nbsp Public domain Public domain false false Bu gorunus butunlukle ictimaiyyete aid melumatlardan meydana gelmesi ve her hansi bir xususi yaradiciya aid olmamasi sebebiyle ictimai varidat olaraq xarakterize edilmekdedir ve muellif huququ qorunmasina daxil deyildir CaptionsazerbaycancaAdd a one line explanation of what this file representsItems portrayed in this filetesvir edirMIME type nbsp ingilisimage svg xml Faylin tarixcesi Faylin evvelki versiyasini gormek ucun gun tarix bolmesindeki tarixlere klikleyin Tarix VaxtKicik sekilOlculerIstifadeciSerh indiki21 48 24 fevral 2023380 280 352 bayt JoKalliauerrecreated human redable more symmetric 22 39 19 noyabr 2022512 373 491 bayt TSamuelCareful recompression via SVGOMG amp vecta io nano amp verified via SVGCheck 14 10 26 iyul 2009384 280 3 KB Watchduck 13 29 26 yanvar 2008615 463 4 KB Watchduck Information Description Source eigene arbeit Date Author Tilman Piesk Permission other versions 16 03 22 yanvar 2008615 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 Fayl kecidleri Bu sekile olan kecidler Coxluqlar nezeriyyesi Faylin qlobal istifadesi Bu fayl asagidaki vikilerde istifade olunur als wikipedia org layihesinde istifadesi Menge Mathematik Mengenlehre am wikipedia org layihesinde istifadesi ስብስብ ውህድ ስብስብ ar wikipedia org layihesinde istifadesi مجموعة رياضيات نظرية المجموعات اتحاد نظرية المجموعات مستخدم Hezzam A ملعب بوابة نظرية المجموعات بوابة نظرية المجموعات صورة مختارة بوابة نظرية المجموعات مقالة مختارة بوابة نظرية المجموعات صورة مختارة 1 بوابة نظرية المجموعات مقالة مختارة 1 bar wikipedia org layihesinde istifadesi Grundlogn vo da Mathematik ba wikipedia org layihesinde istifadesi Kүmәklek be tarask wikipedia org layihesinde istifadesi Mnostva be wikipedia org layihesinde istifadesi Mnostva bg wikipedia org layihesinde 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