80-211 Spring 2003

 

Assignment #11

Due on Monday, April 14th

 

Problem 1: Do problems 1(d) and 1(f) on page 168 of your text.

 

Problem 2: All of the sentences listed below assert that there is at most one thing that has F, show using the rules for equality (and of course the rules for prop and predicate logic) that the sentences are all equivalent. Note, this amounts to showing that the sentences are interderivable.

 

(a) $xFx & "x"y(Fx & Fy x = y)

 

(b) $x(Fx & "y(Fy x = y)

 

(c) $x(Fx & ~$y(Fy & ~(x = y))

 

 

Problem 3: Prove the following sequent using the four quantifier rules and primitive or derived rules of the propositional calculus (Hint: In one of the directions use transposition.)

 

"xFx ├ ~$xGx ↔ ~($x(Fx & Gx) & "y(Gy→Fy))