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.


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
   
 
Ac   Bc
true
A ↔ A
 
  B
 
  Bc
A A
 
 
  Bc
       
 
  Bc
¬A   ¬B
A → ¬B
 
  B
  B
A ← ¬B
 
Ac   B
 
A   B
A ¬B
 
 
A = Bc
A ¬B
 
 
A   B
           
 
Bc
  ¬B
A ← B
 
A
  B
A ↔ ¬B
 
Ac
¬A   B
A → B
 
B
 
B =
A B
 
 
A = c
A ¬B
 
 
A =
A B
 
 
B = c
               
¬B
 
 
  Bc
A
 
 
(A   B)c
¬A
 
 
Ac   B
B
 
B false
 
A true
 
 
A = B
A false
 
B true
 
           
  ¬B
 
 
Ac   Bc
  B
 
 
  B
¬A   B
 
A B
 
       
¬A   ¬B
 
 
  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.


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
 
Venn- and Euler diagrams

Partitions edit

Various files edit