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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. $2^{(n+1)} = \text{O}(2^{n} ).$

All options are correct.

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In option c i tried dividing both sides by 2.. eventually getting  2^n <= c*2^n-1 which is wrong., can you please point out my mistake.

Answer for this question are options A,B,C,D

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