$1.(7$ points$)$ For each of the following two functions f$($n$)$ and g$($n$),$ indicate whether f $=$ O$($g$),$ or f $=($g$)$ or both $($in which case f $=($g$)).($a$)$ f$($n$)=$ n and g$($n$)=$ n$/3$ n$.($b$)$ f$($n$)=100$n$+$lgnandg$($n$)=$n$+($lgn$)2.($c$)$ f$($n$)=10$nlgn and g$($n$)=$ nlg$(10$n$).($d$)$ f$($n$)=10$lgn and g$($n$)=$ lg$($n$2).($e$)$ f$($n$)=$ n$2/$lgn and g$($n$)=$ nlgn$.($f$)$ f$($n$)=$ n$2$n and g$($n$)=3$n$.($g$)$ f$($n$)=2$n and g$($n$)=$