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Question V (10 points): Determine whether the following statements are true or false. If true, prove your answer. If false, provide a counter example. 1. If $f(n)$ is $O(g(n))$, then $3f(n)$ is $O(3g(n))$. 2. $f(n) + g(n)$ is $O(min(f(n), g(n)))$. 3. $2na$ is $O(2^n)$, where $a$ is a constant. Definition: $f(n)$ is said to be in small $o(g(n))$ if $lim_{n \to \infty} \frac{f(n)}{g(n)} = 0$. The small $o()$ notation is usually used to determine whether two functions belong to two different complexity classes or not.

          Question V (10 points): Determine whether the following statements are true or false. If true, prove your answer. If false, provide a counter example.
1. If $f(n)$ is $O(g(n))$, then $3f(n)$ is $O(3g(n))$.
2. $f(n) + g(n)$ is $O(min(f(n), g(n)))$.
3. $2na$ is $O(2^n)$, where $a$ is a constant.
Definition: $f(n)$ is said to be in small $o(g(n))$ if $lim_{n \to \infty} \frac{f(n)}{g(n)} = 0$.
The small $o()$ notation is usually used to determine whether two functions belong to two different complexity classes or not.

Question V (10 points): Determine whether the following statements are true or false. If true, prove your answer. If false, provide a counter example.
1. If f(n) is O(g(n)), then 3f(n) is O(3g(n)).
2. f(n) + g(n) is O(min(f(n), g(n))).
3. 2na is O(2^n), where a is a constant.
Definition: f(n) is said to be in small o(g(n)) if limn →∞(f(n))/(g(n)) = 0.
The small o() notation is usually used to determine whether two functions belong to two different complexity classes or not.

Added by Joshua I.

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