Question V $(10$ points$)$: Determine whether the following statements are true or false. If true, prove your answer.

If false, provide a counter example.

If $f(n)$ is $(g(n)),$ then $3^{f(n)}$ is $(3^{g(n)}).$

$f(n)+g(n)$ is $.$

$2^{na}$ is $O(2^n),$ where $a$ is a constant.

Definition: $f(n)$ is said to be in small $o(g(n))$ if $\underset{n}{lim}\frac{f(n)}{g(n)}=0.$

The small $o()$ notation is usually used to determine whether two functions belong to two different complexity

classes or not.