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Unformatted text preview: Prof. Bjorn Poonen December 14, 2001 MATH 55 FINAL (white) Do not write your answers on this sheet. Instead please write your name, your student ID, your TA’s name, your section time, “white,” and all your answers in your blue books. IMPORTANT: Write your answers to problems 1–12 on the first page or two of your blue book, without the calculations you did to get the answers. To guarantee full credit and to qualify for partial credit, you should show your work on later pages of the blue book, labelled by problem number. Total: 200 pts., 170 minutes. (1) (5 pts. each) For each of (a)-(e) below: If the statement is true (always), write TRUE. Otherwise write FALSE. (Please do not use the abbreviations T and F, since in handwriting they are sometimes indistiguishable.) No explanations are required in this problem. (a) If a function f ( n ) is Θ(2 n ) as n → ∞ , then f ( n ) is also o ( n !) as n → ∞ . (b) For any predicate P ( x ), the propositions ¬∀ xP ( x ) and ∃ xP ( x ) are logically equivalent....
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- Spring '08
- Math, pts, Natural number, Prime number, blue book, Prof. Bjorn Poonen