hw5 - Homework 5 Discrete Mathematics Q1 Exercise 2 p 229...

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Homework 5 Discrete Mathematics Q1. Exercise 2, p. 229 O(n 2 ) Q2. Exercise 16, p.230, a) For this exercise, you can use a calculator, but if the result is too large for the calculator, just express the result as a mathematical formula. log(n) = 8.64*10 15 too big to calculate Q3. Exercise 16, p.230, b) For this exercise, you can use a calculator, but if the result is too large for the calculator, just express the result as a mathematical formula. 1000n =8.64*10 15 n=8640000000000 Q4. Exercise 16, p.230, f) For this exercise, you can use a calculator, but if the result is too large for the calculator, just express the result as a mathematical formula. 2 n =8.64*10 15 Log 2 (8.64*10 15 )= n N=13.098295324461283 Q5. Exercise 40, p.231, a) The worst-case complexity of bubble sort is Θ(n 2 ) when size=n since 1/2n 2 -1/2n When the size is double from n to 2n, the number of comparison changes to: ½(2n) 2 -1/2(2n) = 2n 2 -n

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Q6. Using the definition of divisibility, prove the following: If a, b, and c are integers, where a ≠0, such that a | b and a | c, then a | mb + nc whenever m and n are integers.
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