CSE 463/563, Spring 2005

HOMEWORK #5

Propositional Logic III

Last Update: 18 February 2005

Note: NEW or UPDATED material is highlighted


  1. Prove that the following rules of inference are derivable from our rules of ¬Intro, ¬Elim, ^Intro, ^Elim, vIntro, vElim, >Intro, and >Elim:

    1. Modus Tollens (or "Denying the Consequent"; a variety of >Elim; also, a variety of ¬Intro):

      	From (α > β)
      	and ¬β
      	--------------
      	Infer ¬α
      	

    2. Hypothetical Syllogism (or "Transitivity of the Material Conditional"; a variety of >Intro)

      	From (α > β)
      	and (β > γ)
              --------------
      	Infer (α > γ)
      	

    3. Constructive Dilemma (or "Reasoning by Cases"; a variety of vIntro):

      	From (α v γ)
      	and (α > β)
      	and (γ > δ)
              --------------
      	Infer (β v δ)
      	


  2. Represent the English sentences from HW #3, problem #3, in our language for propositional logic in such a way that you can prove that sentence 3e follows validly from sentences 3a-3d. Then prove it syntactically!


DUE: AT THE BEGINNING OF LECTURE, FRIDAY, FEB. 25



Copyright © 2005 by William J. Rapaport (rapaport@cse.buffalo.edu)
file: 563S05/hw05-2005-02-18.html