Discrete Structures
HW #5
Last Update: 13 February 2009
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All exercises are from §1.5 (rules of inference).
 p. 73: #10 a, d, f
You are given premises and need to find conclusions.
Hint:
 Translate each English sentence into either propositional
logic or firstorder logic.
 Then see what rules of inference can be applied.
(In some cases, more than one can be applied.)
 Finally, translate your conclusion(s) back into English.
 3 points each; total = 9 points.
 p. 73: #14 d
The text gives you an argument in English, and asks you to
"explain which rules of inference are used for each step".
However, instead of doing that, please do the following:
 Translate the argument into FOL;
be sure to give the syntax and semantics of your representation.
 Prove that the argument is valid;
be sure to justify each step as either being a premise or as following
from previous steps by a rule of inference, as we have done in
lecture.
Grading:
 syntax & semantics: 3 points
 translation: 3 points
 proof steps: 3 points
 proof justifications: 3 points
total = 12 points
 p. 73: #16 b
 You are given an argument in English and must determine whether
it is valid. Do this as follows:
 Translate the argument into firstorder logic;
be sure to give the syntax and semantics of your representation.
 Try to prove that it is valid, using rules of inference.
 If you succeed, you're done.
 If you get stuck, then try to show whether it is valid
by using truth tables.
Grading:
 syntax & semantics: 3 points
 translation: 3 points
 determination of validity: 6 points
total = 12 points
Grand total = 33 points.
Tentative grading scheme:
A 33
A 31  32
B+ 29  30
B 27  28
B 25  26
C+ 23  24
C 19  22
C 16  18
D+ 12  15
D 7  11
F 0  6
DUE: AT THE BEGINNING OF LECTURE, FRIDAY, FEBRUARY 20 
Copyright © 2009 by
William J. Rapaport
(rapaport@cse.buffalo.edu)
http://www.cse.buffalo.edu/~rapaport/191/S09/hw05.html20090210