Template:Predicate logic; 2 variables; single; example matrices

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.	Hasse diagram of the implications
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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