Exercises for Chapter 6, part 2

Use the Natural-deduction-proof-checker to prove these claims, and submit your answers within a zipped folder. Do your own work.

1. ∀x(F(x) —> G(x)), F(chuck) |- ∃x(F(x) ^ G(x))
(use ∃i, not ∃e)

2. ∃x(F(x) —> G(x)), ∀y F(y) |- ∃z G(z)
(Use ∃i and ∃e. )

3. ∃x F(x) |− ~(∀x ~F(x))

4. ∀x(F(x) —> ∃y G(x,y)) |- (∃z F(z)) -> (∃z ∃y G(z,y))