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