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PMT1 - Prof Bjorn Poonen October 5 2001 MATH 55 PRACTICE...

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Prof. Bjorn Poonen October 5, 2001 MATH 55 PRACTICE MIDTERM Do not write your answers on this sheet. Instead please write your name, your student ID, your TA’s name, your section time, and all your answers in your blue books. In general, you must show your work to get credit. Total: 100 pts., 75 minutes. (1) For each of (a)-(g) below: If the proposition is true, write TRUE. If the propo- sition 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 circle { ( x, y ) : x R , y R , and x 2 + y 2 = 1 } is a countable set. (b) The propositions p → ¬ q and q → ¬ p are logically equivalent. (c) If p is a prime number, then there is a prime q satisfying p < q < p + 6. (d) There exists a positive integer m such that 30 , 77 , m are pairwise relatively prime. (e) In the RSA cryptosystem, when Bob wants to send Alice a message, it is essential that Bob keeps his encryption method secret. (f) 3 405 13 (mod 7). (g) It is valid to deduce ¬ q , if ¬ p and p q have been proved already.
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