Predicate Logic

_rob

New member
Hi, I am looking to turn three sentences into symbolic language using predicate logic.

First statements
E(x) and A(x,y) are two predicates, where E(x) means "x lives in Paris" and A(x,y) means "x is a friend of y", where x and y are variables representing inhabitants of France.

- There is one person in Paris who is friends with all inhabitants of Paris.

- Pierre does not live in Paris, but he is friends with a resident of Paris.

Second statement
T(x,y) and P(x,y) are two binary predicates, where T(x,y) means "x has the same size as y" and P(x,y) means "x is heavier then y".

- There is one person who is the same height as Olivier, and who is heavier than anyone who is the same height as Olivier.

pka

Elite Member
First statements: E(x) and A(x,y) are two predicates, where E(x) means "x lives in Paris" and A(x,y) means "x is a friend of y", where x and y are variables representing inhabitants of France.
- There is one person in Paris who is friends with all inhabitants of Paris.
- Pierre does not live in Paris, but he is friends with a resident of Paris.
$$\displaystyle (\exists x)(\forall y)[E(x)\wedge (E(y)\Rightarrow A(x,y))]$$
Use $$\displaystyle \mathscr{P}$$ for Pierre. Note that BUT is an additive connective.
$$\displaystyle (\neg E(\mathscr{P})(\exists x)[E(x)\wedge A(\mathscr{P},x)]$$

_rob

New member
Thanks!

It seems though that there is a missing closing parentheses on the second one?
I presume it should be
$$\displaystyle (¬E(P)(∃x))[E(x)∧A(P,x)]$$

Could you help with the other one;
T(x,y) and P(x,y) are two binary predicates, where T(x,y) means "x has the same size as y" and P(x,y) means "x is heavier then y".

- There is one person who is the same height as Olivier, and who is heavier than anyone who is the same height as Olivier.

And can you point me to any online resources to study this properly.

pka

Elite Member
Could you help with the other one;
T(x,y) and P(x,y) are two binary predicates, where T(x,y) means "x has the same size as y" and P(x,y) means "x is heavier then y".
- There is one person who is the same height as Olivier, and who is heavier than anyone who is the same height as Olivier.
And can you point me to any online resources to study this properly.
If you are near a good mathematics library look for symbolic logic textbooks: Copi is the standard. This is a rare book by Durst Language of Mathematics
You need to post some evidence of work on your part. We will check it and give you more help.
In English it should be: "x has the height as y" .