File:Relation1000.svg
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原始文件 (SVG文件,尺寸为384 × 280像素,文件大小:11 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 both sets are empty - elements can be only in their union's complement.
- In propositional logic it tells, that both statements are 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
∅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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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。 |
文件历史
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日期/时间 | 缩略图 | 大小 | 用户 | 备注 | |
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当前 | 2010年5月7日 (五) 22:44 | ![]() | 384 × 280(11 KB) | Watchduck | layout change |
2009年7月26日 (日) 17:58 | ![]() | 384 × 280(25 KB) | Watchduck | ||
2009年4月10日 (五) 16:09 | ![]() | 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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