Set theory
branch of mathematics that studies sets, which are collections of objects
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.
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 