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COT3100exam2sol - COT 3100 Spring 2000 Exam#2 Lecturer Arup...

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COT 3100 Spring 2000 Exam #2 4/4/00 Lecturer: Arup Guha TA: ________________ (Note: You will have 75 minutes for this exam. There are 100 points total to be earned. On some questions you can not earn partial credit. Make sure to read AND follow all the directions. If you need extra room for your work, put it on the last page of the exam before the charts, and CLEARLY number what problem’s work you are continuing.)
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1) (1 pt each) True/False (Assume a, b, and c are positive integers for these questions.) a) 0 | a for all positive integers a. True False b) The total number of prime numbers is infinite. True False c) Euclid’s algorithm prime factorizes an integer. True False d) All surjective functions are also bijections. True False e) If f : A B is a injection, then |A| < |B|. True False f) If a | b and b | c then a | c, for all positive ints a,b and c True False g) The Well Ordering Principle can be used to prove any True False statement that can be proved by induction. h) If a b (mod n) then n | (a 7 – b 7 + 13n) True False i) a 2 0 (mod 4) or a 2 1 (mod 4) True False j) If f(x)=x-a and g(x)=x-b, then f(g(x)) = g(f(x)) True False 2) (2 pts each) Short Answer a) The Fundamental Theorem of Arithmetic states that all positive integers can be uniquely prime factorized.
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