Suppose that f $($n$)$ is $($n$)$ and g$($n$)$ is O$($n$2).$ Prove or disprove the following statements. Note that

to disprove a statement, you need to provide a counter$-$example.

$($a$)$ f $($n$)$ is O$($n$).$

$($b$)$ f $($n$)$ is $(1).$

$($c$)$ f $($n$)$ is O$($n$2).$

$($d$)$ g$($n$)$ is $($n$).$

$($e$)$ g$($n$)$ is $($n$3).$

$($f$)$ g$($n$)$ is O$($n$3).$