Question: 1. You are given an unsorted array of integers, without sorting the array, give an algorithm that returns true if the array has at least

You are given an unsorted array of integers, without sorting the array, give an algorithm that returns true if the array has at least one duplicate value in the array and false if there are no duplicate values. For your algorithm, find big-O, and big-Omega.

Are the integers 42, 53, and 18 pairwise relatively prime? Show your work

3. Given f(0) = 1, f(1) = -1, and f(n+1) = 2*f(n) - f(n-1) find f(5).

4. Using induction, prove that 2 + 4 + ... + 2n = n(n + 1).

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