Determine whether or not the following are true. If true, then provide a derivation showing why. If

false, then provide a derivation showing why. For your proofs use definitions of asymptotic notations. Notice,

in your solutions you are not allowed to use limits$.$ For convenience, you may assume that the logs are in the

base of your choice, but you should specify what base you are using in your derivation.

$($a$)3^2$ is $\backslash$Theta $(1).$

$($b$)(22)^$n is O$(2^$n$).$

$($c$)22^$n is O$(2^$n$).$

$($d$)3$n$^2+$ n $5$ is $\backslash$Theta $($n$^2).$

$($e$)($n$/5)^32$n$^2$ n log n is $\backslash$Theta $($n$^2).$