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5 votes
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Which of the following statement(s) is/are true?

  1. If $\text{T1}(x) = \text{O}(f(x))$ and $\text{T2}(x) = \text{O}(g(x))$ then $\text{T1}(x) + \text{T2}(x) = \text{O} (\max(f(x), g(x))$
  2. If $\text{T}(x) = \text{O}(cf(x)),$ where $c$ is some positive constant then $\text{T}(x) = \text{O}(f(x)).$
  3. If $\text{T1}(x) = \text{O}(f(x))$ and $\text{T2}(x) = \text{O}(g(x))$ then $\text{T1}(x) \ast \text{T2}(x) = \text{O}(f(x) \ast g(x))$
  4. $2^{(n+1)} = \text{O}(2^{n} ).$
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All options are correct.

Answer:

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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.