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Exam_02

# Exam_02 - ArsDigita University Month 2 Discrete Mathematics...

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ArsDigita University Month 2: Discrete Mathematics - Professor Shai Simonson Examination 2 – 100 points Show all work for partial credit. You may use two hours for this exam. After one hour, raise your hand if you feel that the time constraint will be too tight. Name: ______________________________________________________________ 1. /30 2. /28 3. /28 4. /14 Total: /100

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1. Sums (30 points) a. Calculate a formula for the following sum, and prove your formula in any way you like. (a + (a+1) + (a+2) + … + (a+b)). b. The following sum comes up in the analysis of certain sorting algorithms. Find a closed form expression for 1*2 + 2*4 + 3*8 + 4*16 + … + n2 n
2. (28 points) Short Answers – Countability, Sets, Functions a. Is the set of all finite binary trees countable? Explain briefly. b. Prove that log(log x x ) is θ (log x) . c. Assume a domain and range of the real numbers, and state whether each of the following is a function. If it is, then state whether it is onto and whether it is one-one.

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Exam_02 - ArsDigita University Month 2 Discrete Mathematics...

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