Answer each part TRUE or FALSE regarding Big O notation.

a$.2$n $=$ O$($n$).$

b$.$ n$^2=$ O$($n$).$

c$.3^$n $=2^$O$($n$).$

d$.2^(2^$n$)=$ O$(2^(2^$n$)).$

Please also justify each of your true$/$false answers using the Definition: $$ Let f and g be functions f$,$ g : N$->$R$+.$ Say that f$($n$)=$ O$($g$($n$))$ if positive integers c and n$0$ exist such that for every integer n $>=$ n$0,$ f$($n$)<=$ c g$($n$).$ When f$($n$)=$ O$($g$($n$)),$ we say that g$($n$)$ is an upper bound for f$($n$),$ ormore precisely, that g$($n$)$ is an asymptotic upper bound for f$($n$),$ to emphasize that we are suppressing constant factors.$$

In more details: what is f$($n$),$ what is g$($n$),$ whether c and n$0$ exist so that when n$>=$n$0$ that inequation is always true.