File:Relation0000.svg
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![File:Relation0000.svg](http://upload.wikimedia.org/wikipedia/commons/thumb/6/66/Relation0000.svg/384px-Relation0000.svg.png)
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Summary
The circles in this Venn diagram can represent sets in set theory, or statements in propositional logic.
- In set theory it represents the special case, that the whole universe is empty:
- In propositional logic it represents the contradiction
.
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
∅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 | |
---|---|---|---|---|---|
current | 22:17, 7 May 2010 | ![]() | 384 × 280 (11 KB) | Watchduck | layout change |
17:53, 26 July 2009 | ![]() | 384 × 280 (45 KB) | Watchduck | ||
15:37, 10 April 2009 | ![]() | 615 × 463 (4 KB) | Watchduck | {{Information |Description={{en|1=Venn diagrams of the sixteen 2-ary Boolean '''relations'''. Black marks empty areas. There are corresponding diagrams of the sixteen 2-ary Boolean '''operations''' in the Category:Johnston diagrams.}} |Source=Eige |
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