Are the following two statements true or false? If a statement is true, provide a formal proof based on the definitions of the order notations. If a statement is false, provide a counterexample and explain it$.$ Functions f and g are positive functions. a$)$ If h$($n$)=0(1)$ and f$($n$)=2($g$($n$),$ then f$($n$)=12(18($m$).$ We assume that h$($n$)>0)$ for all n$.$ b$)$ If fi$($n$)=0(91($n$))$ and fe$($n$)=0(92($n$)),$ then fi$($n$)-$ fe$($n$)=0(9($n$)-92($n$))$