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.


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
 
Ac  Bc
true
A ↔ A
 
 B
 
 Bc
AA
 
 
 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 =
AB
 
 
A = c
A¬B
 
 
A =
AB
 
 
B = c
¬B
 
 
 Bc
A
 
 
(A  B)c
¬A
 
 
Ac  B
B
 
Bfalse
 
Atrue
 
 
A = B
Afalse
 
Btrue
 
 ¬B
 
 
Ac  Bc
 B
 
 
 B
¬A  B
 
AB
 
¬A  ¬B
 
 
 B
 
 
A = Ac
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.



SyllogismsEdit

PartitionsEdit

Various filesEdit

 

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