For each of the following pairs of functions f$($n$)$ and g$($n$),$ decide whether we have f$($n$)$ in $\backslash$Theta $($g$($n$)),$ or f$($n$)$ in O$($g$($n$)),$ or f$($n$)$ in $($g$($n$)).$ If f$($n$)$ in $\backslash$Theta $($g$($n$)),$ you will not earn any point by selecting f$($n$)$ in O$($g$($n$))$ or f$($n$)$ in $($g$($n$)),$ since f$($n$)$ in $\backslash$Theta $($g$($n$))$ tells more than each of the other two.

$[$ Select $]$

f$($n$)=$

$,$ g$($n$)=$

i$.$

$[$ Select $]$

f$($n$)=$ n$100,$ g$($n$)=1\mathrm{.}001$n$.$

$[$ Select $]$

f$($n$)=(2$

n$)!,$ g$($n$)=2$

n$!.$

$[$ Select $]$

f$($n$)=$

i$2,$ g$($n$)=$

$(2$i$)2.$