Let f(n), g(n) and h(n) be nonnegative functions defined for positive integers…
PYQ GATE 2004Modified — slightly modified from the official paper; see the solution
Let f(n), g(n) and h(n) be nonnegative functions defined for positive integers 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) + h(n) = O(g(n) + h(n))
- B.
f(n) = O(h(n))
- C.
h(n) ≠ O(f(n))
- D.
f(n)h(n) ≠ O(g(n)h(n))
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