File:Relation1110.svg
Archivo original (archivo SVG, nominalmente 384 × 280 píxeles, tamaño de archivo: 4 kB)
Leyendas
Sumario
Resumen[editar]
This Venn diagram is meant to represent a relation between
- two sets in set theory,
- or two statements in propositional logic respectively.
Set theory: The disjoint relation[editar]
The relation tells, that the set is empty: =
It can be written as or as .
It tells, that the sets and have no elements in common:
Example: The set of positive numbers and the set of negative numbers are disjoint: No number is both positive and negative.
But they are not complementary sets, because the zero is neither positive nor negative.
Under this condition several set operations, not equivalent in general, produce equivalent results.
These equivalences define disjoint sets:
Venn diagrams | written formulas |
---|---|
= | |
= | |
= | |
= | |
= | |
= | |
= | |
= |
The sign tells, that two statements about sets mean the same.
The sign = tells, that two sets contain the same elements.
Propositional logic: The contrary relation[editar]
The relation tells, that the statement is never true:
It can be written as or as .
It tells, that the statements and are never true together:
Example: The statements "Number x is positive." and "Number x is negative." are contrary:
They can not be true together. But they are not contradictory, because both statements are false for x=0.
Under this condition several logic operations, not equivalent in general, produce equivalent results.
These equivalences define contrary statements:
Venn diagrams | written formulas |
---|---|
The sign tells, that two statements about statements about whatever objects mean the same.
The sign tells, that two statements about whatever objects mean the same.
Set theory: | subset | disjoint | subdisjoint | equal | complementary |
Logic: | implication | contrary | subcontrary | equivalent | contradictory |
Operations and relations in set theory and logic[editar]
∅c |
A = A |
|||||||||||||
Ac Bc |
true A ↔ A |
A B |
A Bc |
AA |
A Bc |
|||||||||
A Bc |
¬A ¬B A → ¬B |
A B |
A B A ← ¬B |
Ac B |
A B |
A¬B |
A = Bc |
A¬B |
A B |
|||||
Bc |
A ¬B A ← B |
A |
A B A ↔ ¬B |
Ac |
¬A B A → B |
B |
B = ∅ |
AB |
A = ∅c |
A¬B |
A = ∅ |
AB |
B = ∅c | |
¬B |
A Bc |
A |
(A B)c |
¬A |
Ac B |
B |
Bfalse |
Atrue |
A = B |
Afalse |
Btrue | |||
A ¬B |
Ac Bc |
A B |
A B |
¬A B |
AB |
|||||||||
¬A ¬B |
∅ |
A 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. |
more relations | ||||
---|---|---|---|---|
|
Public domainPublic domainfalsefalse |
Esta imagen no es elegible para estar sujeta a derecho de autor y por tanto está en el dominio público, porque consiste enteramente en información que es de propiedad común y carece de autoría original. |
Historial del archivo
Haz clic sobre una fecha y hora para ver el archivo tal como apareció en ese momento.
Fecha y hora | Miniatura | Dimensiones | Usuario | Comentario | |
---|---|---|---|---|---|
actual | 22:50 7 may 2010 | 384 × 280 (4 kB) | Watchduck (discusión | contribs.) | layout change | |
18:01 26 jul 2009 | 384 × 280 (9 kB) | Watchduck (discusión | contribs.) | |||
16:16 10 abr 2009 | 615 × 463 (4 kB) | Watchduck (discusión | contribs.) | {{Information |Description={{en|1=Venn diagrams of the sixteen 2-ary Boolean '''relations'''. Black (0) marks empty areas (compare empty set). White (1) means, that there ''could'' be something. There are corresponding diagrams of th |
No puedes sobrescribir este archivo.
Usos del archivo
Las siguientes páginas usan este archivo:
- Set theory
- File:Relation0000.svg
- File:Relation0001.svg
- File:Relation0010.svg
- File:Relation0011.svg
- File:Relation0100.svg
- File:Relation0101.svg
- File:Relation0110.svg
- File:Relation0111.svg
- File:Relation1000.svg
- File:Relation1001.svg
- File:Relation1010.svg
- File:Relation1011.svg
- File:Relation1100.svg
- File:Relation1101.svg
- File:Relation1110.svg
- File:Relation1111.svg
- File:Venn0000.svg
- File:Venn0001.svg
- File:Venn0010.svg
- File:Venn0011.svg
- File:Venn0100.svg
- File:Venn0101.svg
- File:Venn0110.svg
- File:Venn0111.svg
- File:Venn1000.svg
- File:Venn1001.svg
- File:Venn1010.svg
- File:Venn1011.svg
- File:Venn1100.svg
- File:Venn1101.svg
- File:Venn1110.svg
- File:Venn1111.svg
- Template:Operations and relations in set theory and logic
- Template:Operations and relations in set theory and logic; some
- Category:Boolean functions as relations
Uso global del archivo
Las wikis siguientes utilizan este archivo:
- Uso en ca.wikipedia.org
- Uso en de.wikibooks.org
- Uso en en.wikiversity.org
- Uso en es.wikipedia.org
- Uso en fr.wikiquote.org