File:Relation0001.svg
維基百科,自由的 encyclopedia
此 SVG 檔案的 PNG 預覽的大小:384 × 280 像素。 其他解析度:320 × 233 像素 | 640 × 467 像素 | 1,024 × 747 像素 | 1,280 × 933 像素 | 2,560 × 1,867 像素。
原始檔案 (SVG 檔案,表面大小:384 × 280 像素,檔案大小: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 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 |
|||||||||||
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 |
此檔案不具有著作權,屬於公有領域,因為其所包含之内容均為公共財產且沒有明確的原始作者資訊。 |
檔案歷史
點選日期/時間以檢視該時間的檔案版本。
日期/時間 | 縮圖 | 尺寸 | 使用者 | 備註 | |
---|---|---|---|---|---|
目前 | 2010年5月7日 (五) 22:22 | 384 × 280(11 KB) | Watchduck | layout change | |
2009年7月26日 (日) 17:54 | 384 × 280(40 KB) | Watchduck | |||
2009年4月10日 (五) 15:51 | 615 × 463(4 KB) | Watchduck | {{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 |
檔案用途
沒有使用此檔案的頁面。
全域檔案使用狀況
以下其他 wiki 使用了這個檔案:
- en.wikiversity.org 的使用狀況