File:Relation0100.svg
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原始文件 (SVG文件,尺寸为384 × 280像素,文件大小:8 KB)
摘要
The circles in this Venn diagram can represent sets in set theory, or statements in propositional logic.
- In set theory it tells, that is empty - elements can be only in .
- In propositional logic it tells, that is never true.
In both interpretations is the same as .
Set theory: Logic: |
subset implication |
disjoint contrary |
subdisjoint subcontrary |
equal equivalent |
complementary contradictory |
Operations and relations in set theory and logic
∅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 |
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false A ↔ ¬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 |
此作品不具有版权,属于公有领域,因为其所包含之内容均为公共财产且没有明确的原始作者信息。 |
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当前 | 2010年5月7日 (五) 22:40 | 384 × 280(8 KB) | Watchduck | layout change | |
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2009年4月10日 (五) 16:03 | 615 × 463(4 KB) | Watchduck | ==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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