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GATE | GATE-IT-2004 | Question 55

  • Last Updated : 28 Jun, 2021

Let f(n), g(n) and h(n) be functions defined for positive inter such that
f(n) = O(g(n)), g(n) ≠ O(f(n)), g(n) = O(h(n)), and h(n) = O(g(n)).

Which one of the following statements is FALSE?

(A) f(n) + g(n) = O(h(n)) + h(n))
(B) f(n) = O(h(n))
(C) fh(n) ≠ O(f(n))
(D) f(n)h(n) ≠ O(g(n)h(n))

Answer: (D)


f(n), g(n), h(n) are three functions defined over n
Given f(n) = O(g(n)) but g(n) != O(f(n))
  g(n) = O(h(n)) and h(n) = O(g(n))

So, f(n)*h(n) = O(g(n))*h(n) using above given relations
But it is stated that f(n)*h(n)!=O(g(n))*h(n) which is false
So, answer is option (D).

This solution is contributed by Anil Saikrishna Devarasetty .

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