$[25$

f$($n$).$ Justify your answer using rigorous arguments $($simply stating the answers will result in minimal points awarded.$)$

pts$.]$ For the following pairs of functions g$($n$)$ and f$($n$),$ indicate whether g$($n$)$ is O$,$ o$,\backslash$Omega or $\backslash$Theta of

$($a$)[12$ pts$.]$ g$($n$)=$n and f$($n$)=($log$2$ n$)2($b$)[13$ pts$.]$ g$($n$)=$ n$!$ and f$($n$)=$ nn$.$