Set theory
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.
Contents
Operations on and relations between two setsEdit
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 or statements have complements or negations. They are shown inside this matrix. 
These relations are statements, and have negations. They are shown in a seperate matrix in the box below. 
more relations  


SyllogismsEdit
Syllogisms can be described in the language of set theory.
Barbara 
Celarent 
Darii 
Ferio 
Barbari 
Celaront 

Cesare 
Camestres 
Festino 
Baroco 
Cesaro 
Camestros 

Datisi 
Disamis 
Ferison 
Bocardo 
Felapton 
Darapti 

Calemes 
Dimatis 
Fresison 
Calemos 
Fesapo 
Bamalip 