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Consider two statements below -

  • $\text{S1}:$ For all positive $f(n), f(n) + o(f(n)) = \theta(f(n)).$
  • $\text{S2}:$ For all positive $f(n), g(n)$ and $h(n),$ if $f(n) = O(g(n))$ and $f(n) = \Omega(h(n)),$ then $g(n) + h(n) = \Omega(f(n))$

Which of the following is the correct option.

  1. $\text{S1}$ is True but $\text{S2}$ is False.
  2. $\text{S2}$ is True but $\text{S1}$ is False.
  3. Both are True.
  4. Both are False.
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2 Answers

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Answer is option C  which is both statements are correct

 

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pls upvote if likes the explanation :)

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GO Classes asked May 4, 2022
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If $f(n) = O(g(n))$ and $f(n) = \Omega(g(n)),$ then it is always true that$f(n) = o(g(n)).$$f(n) = \theta(g(n)).$$f(n) = \omega(g(n)).$both A and B are always true.