Question

Let f(n) = n and g(n) = $n^{(1+sinn)}$, where n is a positive integer. Which of the following statement is/are correct?
I. f(n) = O(g(n))
II. f(n) = $\Omega$(g(n))

• A. Only II
• B. Neither I nor II
• C. Both I and II
• D. Only I

Answer 1

The correct option is B Neither I nor II

When ever the value of 'sin n' value is -1, then g(n) = 1. {sin n value ranges from -1 to +1}. Hence f(n) = O(g(n)) is violated. Hence I is false. and when ever the value of 'sin n' is +1, then g(n) = $n^2$
Hence f(n) = $\Omega$(g(n)) is violated. Hence II is false.