{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern