File:Predicate logic; 2 variables; example matrix a2e1.svg

Size of this PNG preview of this SVG file: 230 × 230 pixels. Other resolutions: 240 × 240 pixels | 480 × 480 pixels | 768 × 768 pixels | 1,024 × 1,024 pixels | 2,048 × 2,048 pixels.

Original file (SVG file, nominally 230 × 230 pixels, file size: 15 KB)

This is a file from the Wikimedia Commons. Information from its description page there is shown below.
Commons is a freely licensed media file repository. You can help.

Summary

There are 10 sentences with 8 different meanings, using the loving-relation Lxy and the quantifiers ∀ and ∃:

No column/row is empty:
1. $\forall x\exists yLyx$ : Everyone is loved by someone.	2. $\forall x\exists yLxy$ : Everyone loves someone.

The diagonal is nonempty/full:
5. $\exists xLxx$ : Someone loves himself.
6. $\forall xLxx$ : Everyone loves himself.

The matrix is nonempty/full:
7. $\exists x\exists yLxy$ : Someone loves someone. 8. $\exists x\exists yLyx$ : Someone is loved by someone.
9. $\forall x\forall yLxy$ : Everyone loves everyone. 10. $\forall x\forall yLyx$ : Everyone is loved by everyone.

One row/column is full:
3. $\exists x\forall yLxy$ : Someone loves everyone.	4. $\exists x\forall yLyx$ : Someone is loved by everyone.

Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".

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.

The SVG code is valid.

This predicate was created with Inkscape.

This SVG predicate was uploaded with Commonist.

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Thumbnail	Dimensions	User	Comment
current	18:40, 6 December 2010		230 × 230 (15 KB)	Watchduck

File usage

The following page uses this file:

Talk:Quantification

Global file usage

The following other wikis use this file:

Usage on de.wikipedia.org
- Prädikatenlogik
- Diskussion:Prädikatenlogik/Archiv/1
Usage on de.wikiversity.org
- Prädikatenlogische Formeln
Usage on el.wikipedia.org
- Λογική πρώτου βαθμού
Usage on en.wikiversity.org
- Formulas in predicate logic/2 places
Usage on he.wikipedia.org
- תחשיב הפרדיקטים
- משתמש:גלעד ניר/דף טיוטה

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its original state, some details may not fully reflect the modified file.

Width	230.31496
Height	230.31496