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File:Predicate logic; 2 variables; example matrix e2a1.svg

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Summary

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

No column/row is empty:
1. :
Everyone is loved by someone.
2. :
Everyone loves someone.
The diagonal is
nonempty/full:
5. :
Someone loves himself.
6. :
Everyone loves himself.
The matrix is
nonempty/full:
7. :
Someone loves someone.

8. :
Someone is loved by someone.
9. :
Everyone loves everyone.

10. :
Everyone is loved by everyone.
Hasse diagram of the implications
One row/column is full:
3. :
Someone loves everyone.
4. :
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.
 
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Date/TimeThumbnailDimensionsUserComment
current18:40, 6 December 2010Thumbnail for version as of 18:40, 6 December 2010230 × 230 (12 KB)Watchduck

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