University of Waterloo
Midterm Examination
SOLUTION SET
Term: Winter
Year: 2009
Student Name
UW Student ID Number
Course Abbreviation and Number
CS 245
Course Title
Logic and Computation
Sections
CS245  001, 002
Instructor
Nancy Day
Date of Exam
Thursday, February 12, 2009
Time Period
Start time: 4:30 p.m.
End time: 6:30 p.m.
Duration of Exam
2 hours
Number of Exam Pages
11 pages (including this cover sheet)
Exam Type
Closed book
Additional Materials Allowed
NO ADDITIONAL MATERIALS ALLOWED
•
Write your name and student number at the bottom of every page.
•
Write all solutions on the exam.
•
There are blank truth tables on the last page for use with any question.
•
Good luck everyone!
Question
Mark
Max
Marker
Question
Mark
Max
Marker
1
6
6
12
2
6
7
8
3
8
8
11
4
12
9
14
5
9
10
14
Total
100
Name
UW Student ID
(page 1 of 11)
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1
(6 Marks) Short Answer
1. If using proof procedure A, I’m able to prove a formula is a tautology, and using proof proce
dure B, I’m able to prove the same formula is a contradiction, which of the following might
be the problem? Check
ALL
boxes that might cause this problem.
√
proof procedure A is unsound
square
proof procedure A is incomplete
√
proof procedure B is unsound
square
proof procedure B is incomplete
2. If a closed predicate logic formula is not a contradiction, is it satisfiable? Yes
3. Who invented natural deduction?
Gentzen
4. If the premises of an argument are inconsistent, which of the following statements is correct?
square
The argument is invalid.
√
The argument is valid.
square
We don’t have enough information to determine if the argument is valid or invalid.
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 Spring '08
 A
 Logic, student id

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