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final-f05 - York University Faculty of Pure and Applied...

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Unformatted text preview: York University Faculty of Pure and Applied Science, Faculty of Arts, Atkinson Faculty MATH 1090 Final Examination, December 2005 Sections A (Tourlakis) and B (Farah) NAME ( print in ink ): (Family) (First) SIGNATURE ( in ink ): SECTION ( in ink ): STUDENT NUMBER( in ink ) Instructions: 1. Please read all the instructions carefully before you start dealing with the questions. 2. You have 3 hours. CLOSED BOOK. No Notes allowed beyond the distributed at the Exam Logic Facts pages. 3. If you run out of space, continue on the backs of pages. It is not allowed to add or remove pages. 4. The Predicate Calculus Axioms and Primitive Rules of Inference must be the ones from class, and are listed on the distributed Logic Facts pages. No substitutes are accepted! 5. Any theorems or metatheorems proved in class or assigned as homework are ready to be used “off the shelf”— unless you are asked not to use some known result . Any other “provable” formula (or “rule”) that you may want to use needs a proof. Question Pts. Marks 1 4 2 4 3 10 4 10 5 5 6 10 7 12 8 10 9 5 10 5 Total 75 MATH 1090 Final Exam December 2005 Question 1. (4 MARKS) (a) Use a truth table, or a shortcut of one, to show that | = taut parenleftBig A ∧ B ∧ C ⇒ D parenrightBig ≡ parenleftBig A ⇒ ( B ⇒ ( C ⇒ D )) parenrightBig...
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final-f05 - York University Faculty of Pure and Applied...

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