Assume you have functions f and g such that f (n) is O(g(n)). For each of the following statements, decide whether you think it is true or false and give a proof or counterexample.
(a) log2 f (n) is O(log2 g(n)).
(b) 2f (n) is O(2g(n)).
(c) f (n)2 is O(g(n)2).
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