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

SummaryEdit

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 (a.k.a. Tilman Piesk)

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