As I recall in propositional logic, it was possible to draw truth tables for the arguments such as for:
(P ∨ R) [I live in Paris or I live in Rome]
Therefore, (~P ⊃ R) [If I don't live in Paris then I live in Rome]
You have a truth table given as:
+---+----+---------+------------+
| P | R | (P ∨ R) | (~P ⊃ R) |
+---+----+---------+------------+
| 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 |
| 0 | 0 | 0 | 0 |
+---+----+---------+------------+
But when you have argument in predicate logic such as:
~(∃x)Fx
Therefore, (x)~(Fx • Gx)
Can the similar form of truth table be derived to test for validity rather than a proof solving approach?
And, one of my other quick question is: Is it possible to convert the above argument (with P and R) given in Propositional logic into Predicate logic or it can only be written in propositional logic?