Homework 9

Due Thursday, April 27 at the start of class.

Prove the following sequents of predicate logic:

1. (x)(Fx -> Gx), (x)(Hx -> -Gx) |- (x)(Fx -> -Hx)
2. (x)((Fx v Gx) -> Hx), (Ex)-Hx |- (Ex)-Fx
3. (x)(Fx <-> Gx) -||- (x)Fx <-> (x)Gx (note both directions)