Question: Given a positive increasing functions f(n), decide whether each of the following statements holds. Justify each of your answers, that is, prove the statement if

Given a positive increasing functions f(n), decide whether each of the

Given a positive increasing functions f(n), decide whether each of the following statements holds. Justify each of your answers, that is, prove the statement if your answer is yes, and provide a counterexample if your answer is no. (i) If f(n) = O(n), then lg(f(n)) = O(lg n). (ii) For any positive increasing functions f(n), we always have f(2n) = Theta (f(n))

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