Set theory
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English: Set theory is a branch of Mathematics.
It's regarded the foundation of mathematics, and closely related with logic.
It's regarded the foundation of mathematics, and closely related with logic.
Operations on and relations between two sets[edit]
The Venn diagrams in the left matrix represent set operations  e.g. the intersection ,
those in the right matrix represent set relations  e.g. the subset relation , more usually represented by an Euler diagram:
The set theoretic descriptions are over the Venn diagrams:
_{ } ∅^{c} 
_{ } A = A 

_{ } A^{c} B^{c} 
true ^{A ↔ A} 
_{ } A B 
_{ } A B^{c} 
AA ^{ } 
_{ } A B^{c} 

_{ } A B^{c} 
¬A ¬B ^{A → ¬B} 
_{ } A B 
A B ^{A ← ¬B} 
_{ } A^{c} B 
_{ } A B 
A¬B ^{ } 
_{ } A = B^{c} 
A¬B ^{ } 
_{ } A B 

_{ } B^{c} 
A ¬B ^{A ← B} 
_{ } A 
A B ^{A ↔ ¬B} 
_{ } A^{c} 
¬A B ^{A → B} 
_{ } B 
_{ } B = ∅ 
AB ^{ } 
_{ } A = ∅^{c} 
A¬B ^{ } 
_{ } A = ∅ 
AB ^{ } 
_{ } B = ∅^{c}  
¬B ^{ } 
_{ } A B^{c} 
A ^{ } 
_{ } (A B)^{c} 
¬A ^{ } 
_{ } A^{c} B 
B ^{ } 
Bfalse ^{ } 
Atrue ^{ } 
_{ } A = B 
Afalse ^{ } 
Btrue ^{ }  
A ¬B ^{ } 
_{ } A^{c} B^{c} 
A B ^{ } 
_{ } A B 
¬A B ^{ } 
AB ^{ } 

¬A ¬B ^{ } 
_{ } ∅ 
A B ^{ } 
_{ } A = A^{c} 

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  


Syllogisms[edit]
Syllogisms can be described in the language of set theory.
1  Barbara 
Barbari 
Darii 
Ferio 
Celaront 
Celarent 

2  Festino 
Cesaro 
Cesare 
Camestres 
Camestros 
Baroco 

3  Darapti 
Datisi 
Disamis 
Felapton 
Ferison 
Bocardo  
4  Bamalip 
Dimatis 
Fesapo 
Fresison 
Calemes 
Calemos 
Partitions[edit]
Various files[edit]
Venn 0000 0001.svg
All 256 Venn diagrams of this kind can be found here