CSE 472/572, Spring 2002

HW #5: PROPOSITIONAL LOGIC

Last Update: 5 March 2002

Note: NEW material is highlighted

  1. Russell & Norvig, Ch. 6, p. 180: #6.2, Distributivity of tex2html_wrap_inline21 over tex2html_wrap_inline23, De Morgan's Law (first one)

  2. Russell & Norvig, Ch. 6, p. 181: #6.4

  3. Russell & Norvig, Ch. 6, p. 181: #6.5

    NEW
    In doing this problem, you might find the following additional rules of inference for the natural-deduction system that I am introducing in lecture to be useful (though note that you do not need anything that is not in Ch. 6):

    vIntro:  From P                From Q
             -----------           -----------
             Infer (PvQ)           Infer (PvQ)
    
    
    vElim:   From (PvQ)            From (PvQ)
             and  -P               and  -Q
             ----------            ----------
             Infer Q               Infer P
    
    
    <=>Intro:  From (P => Q)       From (P => Q)
               and  (Q => P)       and  (Q => P)
               ---------------     ---------------
               Infer (P <=> Q)     Infer (Q <=> P)
    
    
    <=>Elim:   From (P <=> Q)      From (P <=> Q)
               --------------      --------------
               Infer (P => Q)      Infer (Q => P)
    

    Also: You can't use natural deduction (or any other syntactic proof-technique) to prove that you can't prove something. But you can prove that you can't prove something, by using semantic proof-techniques, such as truth tables or Wang's Algorithm.

    For more details on the natural-deduction system introduced in lecture, see:

  4. Let's add to the definition of a well-formed formula of propositional logic the 3-place connective:
    if P then Q else R

    (a) Give a truth table for it.

    (b) Define it in terms of tex2html_wrap_inline31, tex2html_wrap_inline21, and tex2html_wrap_inline23. (I.e., your definition will use some or all of those binary connectives.)

DUE AT START OF LECTURE: WED., MAR. 6



Copyright © 2002 by William J. Rapaport (rapaport@cse.buffalo.edu)
file: 572/S02/hw05.05mr02.html