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Unformatted text preview: Midterm REVIEW MATH 224 1. Review the relevant sections from Chapters 1 – 4 in our text, quizzes, and written assignments. 2. Construct a truth table for p ⊕ q → q . 3. Construct a truth table for p → ( q ∧ ¬ r ). 4. Sort the following in order by Θ, (smallest to largest). n lg n, n 5 , 2 3 lg n , 2 n , 3 n 3 + n 5 , lg n 5 , n . 9 5. Explain what it means for a set of operators, e.g., ∧ , ∨ , and ¬ to be a functionally complete set of propositional operators. 6. Convert the following proposition into conjuctive normal form: ( p ∨ q ) → ( r ∧ ¬ s ). 7. Using a truth table, show that the two propositions below are equivalent. ( a ∧ b ) ∨ ( a ∧ c ) (( a → b ) ∨ ( a → c )) ∧ a 8. What rule of inference is used in the following. If there are more than 100 CS majors a course in advanced algorithms will be offered during the spring semester. If advanced algorithms is offered, at least one student will go to the chair and complain that CS is too hard. There are more than 100 CS majors at SIUE, therefore at least one student will go to the chair and complain that CS is too hard.at least one student will go to the chair and complain that CS is too hard....
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This note was uploaded on 08/26/2009 for the course MATH 224 taught by Professor Waxman during the Fall '08 term at Southern Illinois University Edwardsville.
- Fall '08