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010_2007_midterm

# 010_2007_midterm - CS3234 Logic and Formal Systems Midterm...

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CS3234 Logic and Formal Systems Midterm Examination Questions 20/09/2007 This examination question booklet has 6 pages, including this cover page, and contains 17 questions. Answer all questions. All questions have equal weight. You have 45 minutes to complete the examination. Use a B2 pencil to fill up the provided MCQ form. Leave Section A blank. Fill up Sections B and C. After finishing, place the MCQ sheet on top of the question sheet and leave both on the table, when you exit the room. 1

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Question 1 : In ternary logic, there are three “truth values” instead of the usual two values T and F as in boolean logic. How many different binary relations exist in ternary logic? 1 a3 a2 a0 a1 A 2 2 3 = 256 1 a3 a2 a0 a1 B 2 3 2 = 512 1 a3 a2 a0 a1 C 3 2 3 = 6561 1 a3 a2 a0 a1 D 3 3 2 = 19683 1 a3 a2 a0 a1 E None of the above Answer 1 : 1 a3 a2 a0 a1 D There are 3 2 rows in each truth table. For each row in each truth table, there are 3 values to pick from. Thus there are 3 3 2 truth tables. Question 2 : Is there a formula in the propositional calculus A = A 1 op A 2 where op is a boolean operator and A 1 and A 2 are valid formulas, such that A is unsatisfiable? 2 a3 a2 a0 a1 A Yes 2 a3 a2 a0 a1 B No Answer 2 : 2 a3 a2 a0 a1 A Example: A 1 A 2 Question 3 : Is there a formula in the propositional calculus A = A 1 op A 2 where op is a boolean operator and A 1 and A 2 are valid formulas, such that A is satisfiable and falsifiable? 3 a3 a2 a0 a1 A Yes 3 a3 a2 a0 a1 B No Answer 3 : 3 a3 a2 a0 a1 B If both A 1 and A 2 are valid (in every truth assignment), their combination must be valid or unsatisfiable.
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