Tutorial 15: Elementary derivations in predicate logic

Logical System


The Tutorial

The propositional rules of derivation carry over unchanged into Predicate Logic



Exercises to accompany Predicate Tutorial 5

Exercise 1 (of 1).


The propositional rules of inference are used unchanged in predicate logic.


a) Fa ∴ ∼ ∼ Fa
b) ∴ ∼ (Fb∧ ∼ Fb)
c) ∼ Fm∧ ∼ Gn∴ ∼ (Fm∨Gn)
d) (Fa∧Fa)∨(Gb∧Gb)∴ Fa∨Gb
e) Fb⊃(Ga⊃Hc), Fb⊃Ga ∴ Fb⊃Hc
f) Fa∨Gb, Gb⊃Hd ∴ ( ∼ Fa⊃Hd)
g) (Fa⊃Gb)∧(Gb⊃Fa) ∴ Fa≡Gb

If you decide to use the web application for the exercises you can launch it from here Deriver [Gentzen] — username 'logic' password 'logic'. Then either copy and paste the above formulas into the Journal or use the Deriver File Menu to Open Web Page with this address https://softoption.us/test/easyDeriver/CombinedExercisesEasyDGentzen.html . 


You may need to set some Preferences for this.

  • you can check that the parser is set to gentzen.