File:Predicate logic; 2 variables; example matrix e(12).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. $\forall x\exists yLyx$ : 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".

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