White MT - Prof Bjorn Poonen MATH 55 MIDTERM(white Do not...

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Prof. Bjorn Poonen October 16, 2001 MATH 55 MIDTERM (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. 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 value of ( - 141) mod 8 is - 5. (b) The function 3 n 2 log n + 5 n (log n ) 4 is O ( n 3 ). (c) The ceiling function f ( x ) = d x e , considered as a function from R to R , has an inverse function. (d) The set { 1 , 2 , 3 } × Z is countable. (e) The proposition x y ( x y ) is true, when the universe of discourse is the set of natural numbers.
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