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İzahVenn0001.svg
Intersection math
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The source code of this SVG is invalid due to 12 errors.
This W3C-invalid icon was created with Inkscape…important.
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
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= }}
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Fayl Faylin tarixcesi Istifade edilen sehifeler Faylin qlobal istifadesi MetamelumatlarBu SVG faylin PNG formatindaki bu gorunusunun olcusu 384 280 piksel Diger olculer 320 233 piksel 640 467 piksel 1 024 747 piksel 1 280 933 piksel 2 560 1 867 piksel Faylin orijinali 8206 SVG fayli nominal olaraq 384 280 piksel faylin olcusu 3 KB Bu fayl Vikimedia Commons dadirve diger layihelerde istifade edile biler Faylin tesvir sehifesine get Xulase IzahVenn0001 svg Intersection mathMenbe This file is lacking source information Please edit this file s description and provide a source Muellif This file is lacking author information Icaze Faylin tekrar istifadesi Public DomainSVG genesisInfoField The source code of this SVG is invalid due to 12 errors This W3C invalid icon was created with Inkscape important 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 Ac displaystyle scriptstyle cup Bc trueA A A displaystyle scriptstyle cup B A displaystyle scriptstyle subseteq Bc A displaystyle scriptstyle Leftrightarrow A A displaystyle scriptstyle supseteq Bc A displaystyle scriptstyle cup Bc A displaystyle scriptstyle lor BA B A D displaystyle scriptstyle Delta B A displaystyle scriptstyle lor BA B Ac displaystyle scriptstyle cup B A displaystyle scriptstyle supseteq B A displaystyle scriptstyle Rightarrow B A Bc A displaystyle scriptstyle Leftarrow B A displaystyle scriptstyle subseteq B Bc A displaystyle scriptstyle lor BA B A A displaystyle scriptstyle oplus BA B Ac A displaystyle scriptstyle lor BA B B B A displaystyle scriptstyle Leftarrow B A c A displaystyle scriptstyle Leftrightarrow B A A displaystyle scriptstyle Rightarrow B B c B A displaystyle scriptstyle cap Bc A A D displaystyle scriptstyle Delta B c A Ac displaystyle scriptstyle cap B B B displaystyle scriptstyle Leftrightarrow false A displaystyle scriptstyle Leftrightarrow true A B A displaystyle scriptstyle Leftrightarrow false B displaystyle scriptstyle Leftrightarrow true A displaystyle scriptstyle land B Ac displaystyle scriptstyle cap Bc A displaystyle scriptstyle leftrightarrow B A displaystyle scriptstyle cap B A displaystyle scriptstyle land B A displaystyle scriptstyle Leftrightarrow B A displaystyle scriptstyle land B A displaystyle scriptstyle land B A AcfalseA A A displaystyle 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 relationsThe 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 Public domain Public domain false falseBu 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 Faylin tarixcesi Faylin evvelki versiyasini gormek ucun gun tarix bolmesindeki tarixlere klikleyin Tarix VaxtKicik sekilOlculerIstifadeciSerh indiki14 06 26 iyul 2009384 280 3 KB Watchduck 14 05 26 iyul 2009384 280 3 KB Watchduck 13 24 26 yanvar 2008615 463 4 KB Watchduck Information Description Source eigene arbeit Date Author Tilman Piesk Permission other versions 15 57 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 14 26 22 yanvar 2008480 360 3 KB Watchduck Information Description Source Date Author Permission other versions Istifade edilen sehifeler Bu sekile olan kecidler Coxluqlar nezeriyyesi Faylin qlobal istifadesi Bu fayl asagidaki vikilerde istifade olunur als wikipedia org layihesinde istifadesi Menge Mathematik 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