80-211 Spring 2003

Assignment #7

Due on Friday, March, 7th.

**Note**: For all
these problems you can use the derived rules of the propositional calculus, but
you may *not* use any derived rules of
predicate logic.

Problem 1 (1 pt): Do problem 1-(c) on page 116 of your book.

Problem 2 (4 pts): On page 117 do problems (a), (d), (f), (g) of 2(i).

Problem 3 (5 pts): Prove the following sequents, and note that for (d) you must prove both directions:

(a) (x)(Fx→Gx) ├ ($x)Fx → ($x)Gx

(b) (x)~Fx ├ ~($x)Fx

(c) ~($x)(Fx & Gx) ├
(x)(Fx→ ~Gx)

(d) ($x)~Fx ┤├ ~(x)Fx