Exam20080910

Exam20080910 - a Someone at UGA is a grad student a TA and...

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Csci 2610, Fall 2008 Exam 1 2008.09.10 1 Name: _________________________________ Seat:_______________ Exam 1 has 9 questions worth a total of 75 points. Please make certain you have all 4 pages. You will have 50 minutes to complete the exam. 1. (5 points) In one sentence, define a proposition. 2. (10 points) Construct a truth table for (p (p q)) (q   p) and use the table to explain why the statement is or is not a tautology. 3. (10 points) By using only the logical identities , show that ((p q)   q) p is a tautology.
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Csci 2610, Fall 2008 Exam 1 2008.09.10 2 4. (10 points) Use a symbolic proof to derive q from the premises (p q) r, r s, and s. 5. (5 points) Let G(x) be the statement x is a grad student . Let Q(x) be the statement x is a TA. Let R(x) be the statement x is a robot . Assume that the universe of discourse consists of all people at UGA. Express the following statements using predicates, connectives, and quantifiers:
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Unformatted text preview: a) Someone at UGA is a grad student, a TA, and a robot. b) No one at UGA is a grad student, a TA, and a robot. c) Everyone at UGA is a grad student and a TA, but not a robot. Csci 2610, Fall 2008 Exam 1 2008.09.10 3 6. (10 points) Use a symbolic proof to derive x(R(x) S(x)) from the premises x(P(x) (Q(x) S(x)) and x(P(x) R(x)). 7. (5 points) What is the result of the following bitwise operations? (0111 1100 0101 0000) (1100 0100) 8. (5 points) Demonstrate that x P(x) is not equivalent to x P(x) by providing a counterexample. The counterexample should consist of a definition and a universe of discourse for the predicate P(x) for which only one of the above statements is true. Csci 2610, Fall 2008 Exam 1 2008.09.10 4 9. (15 points) Prove that if n is odd, then n 2 + n is even....
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Exam20080910 - a Someone at UGA is a grad student a TA and...

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