Tutorial 15: Elementary derivations in predicate logic

Logical System

copi

The Tutorial

The propositional rules of derivation carry over unchanged into Predicate Logic

Exercises to accompany Predicate Tutorial 5

Exercise 1 (of 1).

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

Derive

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