CIS301 Exercises for Chapter 6, part 2
10 points.
Due Monday, April 21
Use the Natural-deduction-proof-checker to prove the following sequents, and upload your answers in a zipped folder to K-State Online.
-
1.
∀x(F(x) —> G(x)), F(chris) |- ∃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))