The statements below show some features of $$Big$-$Oh$$ notation for the functions f $$ f $($n$)$ and g $$ g$($n$).$

Determine whether each statement is TRUE or FALSE and correct the formula in the latter case. $[$Read

CORMEN Section $3\mathrm{.}1$ to learn more about the rules if you have not done so already.$]$

Statement Is it TRUE

or FALSE?

If it is FALSE then write

the correct formula

Rule of sums:

O$($f $+$ g$)=$ O$($f $)+$ O$($g$)$

Rule of products:

O$($f $$ g$)=$ O$($f $)$ O$($g$)$

Transitivity:

if g $=$ O$($f $)$ and h $=$ O$($f $)$ then g $=$ O$($h$)$

$5$n $+8$n$2+100$n$3=$ O$($n$4)$

$5$n $+8$n$2+100$n$3=$ O$($n$2$logn$)$