Let A $=\{$n$1\mathrm{.}5,2$ log n$,($n $+5)3,2$n$+1,22$n$\},$ and

B$=\{$n$3,$ n$2$logn$,2$n$\}.$

For each of the functions f$($n$)$ in set A$,$ list all the functions g$($n$)$ from set B such that

$1.$ f$($n$)=$ O$($g$($n$))2.$ f$($n$)=$ o$($g$($n$))3.$ f$($n$)=\backslash$Omega $($g$($n$))4.$ f$($n$)=\backslash$Theta $($g$($n$))$