For functions A and B and constant c $>1,$ indicate which of $\{$A $=$ O$($B$),$A $=\backslash$Omega $($B$),$A $=\backslash$Theta $($B$)\}$ holds. Here, we use the notation that log$2=$ lg$.$ Hint: for these problems it is useful to know some mathematical identities. See CLRS section $3\mathrm{.}2$ or CLRS Standard Notations and Common Functions in HuskyCT lecture notes.

$($a$)$ A$=$nc$,$B$=$cn

$($b$)$ A $=$ nlg$($c$),$ B $=$ clg$($n$)$

$($c$)$ A $=$ lg$($n$!),$ B $=$ lg$($nn$).$ For this problem, you will find Stirling$$s approximation useful: n$!=2\backslash$pi nnn$1+\backslash$Theta $1.$

$($d$)$ A$=33$n$,$B$=3$n$2$