GATE | Sudo GATE 2020 Mock II (10 January 2019) | Question 25

Let functions f and g such that f(n) is O(g(n)) and following statements:

I. log f(n) is O(log g(n))
II. 2f(n) is O(2g(n))
III. f(n)2 is O(g(n)2) 

Which of the following statement(s) is/are false ?
(A) I and II
(B) I and III
(C) II and III
(D) All I, II, III

Answer: (A)

Explanation: Only statement (III) f(n)2 is O(g(n)2) is correct.

Option (A) is true.

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