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cs245-midterm-exam-soln - University of Waterloo Midterm...

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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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