File:Relation0101.svg
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![File:Relation0101.svg](https://upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Relation0101.svg/384px-Relation0101.svg.png?20100507224119)
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Summary
[edit]The circles in this Venn diagram can represent sets in set theory, or statements in propositional logic.
- In set theory it tells, that the left set is the whole universe (that it's complement is empty).
- In propositional logic it tells, that the left statement is always true (and it's negation never true).
In both interpretations
is the same as
.
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Set theory: Logic: |
subset implication |
disjoint contrary |
subdisjoint subcontrary |
equal equivalent |
complementary contradictory |
Operations and relations in set theory and logic
[edit] ∅c |
A = A |
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Ac |
true A ↔ A |
A |
A |
A |
A |
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A |
¬A A → ¬B |
A |
A A ← ¬B |
Ac |
A |
A |
A = Bc |
A |
A |
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Bc |
A A ← B |
A |
A A ↔ ¬B |
Ac |
¬A A → B |
B |
B = ∅ |
A |
A = ∅c |
A |
A = ∅ |
A |
B = ∅c | |
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¬B |
A |
A |
(A |
¬A |
Ac |
B |
B |
A |
A = B |
A |
B | |||
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A |
Ac |
A |
A |
¬A |
A |
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¬A |
∅ |
A |
A = Ac |
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false A ↔ ¬A |
A |
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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 | ||||
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Public domainPublic domainfalsefalse |
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This work is ineligible for copyright and therefore in the public domain because it consists entirely of information that is common property and contains no original authorship. |
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 22:41, 7 May 2010 | ![]() | 384 × 280 (7 KB) | Watchduck (talk | contribs) | layout change |
17:56, 26 July 2009 | ![]() | 384 × 280 (33 KB) | Watchduck (talk | contribs) | ||
16:05, 10 April 2009 | ![]() | 615 × 463 (4 KB) | Watchduck (talk | contribs) | ==Description== {{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 correspondin |
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File usage on Commons
The following 34 pages use this file:
- 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