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c-cl-SeLo

# c-cl-SeLo - Sets and Logic MHF3202 SeLo-C Prof JLF King...

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Sets and Logic MHF3202 SeLo-C Prof. JLF King 31Dec2009 C1: Essay, on your own paper, triple-spaced. Please prove: Thm : There are ly many prime numbers. Start with. . . Proof: FTSOContradiction, suppose p 1 < p 2 < · · · < p k < · · · < p L - 1 < p L * : is a list of all prime numbers. I will now produce a prime q which differs from every member of ( * ), as follows. ( Continue your proof from here. ) Short answer. For (C2) and (C3) , show no work; please fill-in each blank on the problem-sheet. C2: Please write DNE in a blank if the described object does not exist or if the indicated operation cannot be performed. z Prof. King believes that writing in com- plete, coherent sentences is crucial in communicating Mathematics, improves posture, and whitens teeth. Circle one: True! Yes! wH’at S a?sEnTENcE a Repeating decimal 0 . 1 14 equals n d , where posints n d are n = . . . . . . . . . . . . . . and d = . . . . . . . . . . . . . . . b Note that Gcd(15 , 21 , 35) = 1. Find particular integers S, T, U so that 15 S + 21 T + 35 U = 1: S = . . . . . . . . . . , T = . . . . . . . . . . , U = . . . . . . . . . . . [ Hint: Gcd ` Gcd(15 , 21) , 35 ´ = 1. ] c The number of ways of having 3 objects from 6 distinct types is s 3 6 { Binom === coeff . . . . . Single ==== integer . . . . . . . And q 3 6 y = q K L y , where K = . . . . . . . and L = . . . . . . . . d On Z + , write x \$ y IFF Gcd( x, y ) > 2. So \$ is Transitive T F .
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