PA of Algorithms Q42

42Let f (n), g(n) and h(n) be 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?

Option : D
Explanation :
Given,
f (n) = O (g (n))
g (n) ≠ O (f (n))
g (n) = O (h (n))
h (n) = O (g (n))
So conclusion is
f (n) < g (n) = h (n) { in terms of growth rate}
So
(A) f (n) + g (n) = O (h(n) + h (n)) is true.
(B) f (n) = O (h (n)) is true.
(C) h (n) ≠ O (f (n)) is true.
(D) f (n) * h(n) ≠ O (g(n) * h (n) is false.

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