There are 10 sentences with 8 different meanings, using the lovingrelation 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 (a.k.a. Tilman Piesk)
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