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Yellow MT - Prof Bjorn Poonen MATH 55 MIDTERM(yellow Do not...

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Prof. Bjorn Poonen October 16, 2001 MATH 55 MIDTERM (yellow) Do not write your answers on this sheet. Instead please write your name, your student ID, your TA’s name, your section time, “yellow,” and all your answers in your blue books. Total: 100 pts., 75 minutes. (1) (5 pts. each) For each of (a)-(g) below: If the proposition is true, write TRUE. If the proposition is false, 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) The set { 0 , 1 } * of bit strings of finite length is a countable set. (b) The proposition x y ( x y ) is true, when the universe of discourse is the set of natural numbers. (c) The numbers 34 , 35 , 36 are pairwise relatively prime. (d) There are infinitely many integers x satisfying both x 12 (mod 99) and x 16 (mod 100). (Hint: you don’t need to solve this system.) (e) The function 3 n 2 log n + 5 n (log n ) 4 is O ( n 3 ).
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