80-211 Spring 2003

Assignment #11

Due on Monday, April
14^{th}

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))