Set theory

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 setsEdit

The Venn diagrams in the left matrix represent set operations - e.g. the intersection Venn0001.svg,
those in the right matrix represent set relations - e.g. the subset relation Relation1011.svg, more usually represented by an Euler diagram: Venn A subset B.svg
The set theoretic descriptions are over the Venn diagrams:

 
c
          
A = A
1111 1111
 
Ac \scriptstyle \cup Bc
true
A ↔ A
 
\scriptstyle \cup B
 
\scriptstyle \subseteq Bc
A\scriptstyle \LeftrightarrowA
 
 
\scriptstyle \supseteq Bc
1110 0111 1110 0111
 
\scriptstyle \cup Bc
¬A \scriptstyle \or ¬B
A → ¬B
 
\scriptstyle \Delta B
\scriptstyle \or B
A ← ¬B
 
Ac \scriptstyle \cup B
 
A \scriptstyle \supseteq B
A\scriptstyle \Rightarrow¬B
 
 
A = Bc
A\scriptstyle \Leftarrow¬B
 
 
A \scriptstyle \subseteq B
1101 0110 1011 1101 0110 1011
 
Bc
\scriptstyle \or ¬B
A ← B
 
A
\scriptstyle \oplus B
A ↔ ¬B
 
Ac
¬A \scriptstyle \or B
A → B
 
B
 
B =
A\scriptstyle \LeftarrowB
 
 
A = c
A\scriptstyle \Leftrightarrow¬B
 
 
A =
A\scriptstyle \RightarrowB
 
 
B = c
1100 0101 1010 0011 1100 0101 1010 0011
¬B
 
 
\scriptstyle \cap Bc
A
 
 
(A \scriptstyle \Delta B)c
¬A
 
 
Ac \scriptstyle \cap B
B
 
B\scriptstyle \Leftrightarrowfalse
 
A\scriptstyle \Leftrightarrowtrue
 
 
A = B
A\scriptstyle \Leftrightarrowfalse
 
B\scriptstyle \Leftrightarrowtrue
 
0100 1001 0010 0100 1001 0010
\scriptstyle \and ¬B
 
 
Ac \scriptstyle \cap Bc
\scriptstyle \leftrightarrow B
 
 
\scriptstyle \cap B
¬A \scriptstyle \and B
 
A\scriptstyle \LeftrightarrowB
 
1000 0001 1000 0001
¬A \scriptstyle \and ¬B
 
 
\scriptstyle \and B
 
 
A = Ac
0000 0000
false
A ↔ ¬A
A\scriptstyle \Leftrightarrow¬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

Syllogisms can be described in the language of set theory.

Modus Barbara.svg
Barbara
Modus Celarent.svg
Celarent
Modus Darii.svg
Darii
Modus Ferio.svg
Ferio
Modus Barbari.svg
Barbari
Modus Celaront.svg
Celaront
Modus Cesare.svg
Cesare
Modus Camestres.svg
Camestres
Modus Festino.svg
Festino
Modus Baroco.svg
Baroco
Modus Cesaro.svg
Cesaro
Modus Camestros.svg
Camestros
Modus Datisi.svg
Datisi
Modus Disamis.svg
Disamis
Modus Ferison.svg
Ferison
Modus Bocardo.svg
Bocardo
Modus Felapton.svg
Felapton
Modus Darapti.svg
Darapti
Modus Calemes.svg
Calemes
Modus Dimatis.svg
Dimatis
Modus Fresison.svg
Fresison
Modus Calemos.svg
Calemos
Modus Fesapo.svg
Fesapo
Modus Bamalip.svg
Bamalip
Venn- and Euler diagrams

PartitionsEdit

Various filesEdit

 

Last modified on 8 May 2012, at 10:16