For each of the following $5$ statements, select True $($if you believe the statement is true$)$ and False $($if you believe the statement is false$).($a$)[$ Select $]$ If f$($n$)$ O$($n$2)$ and g$($n$)($n$),$ then f$($n$)+$ n $\backslash$times g$($n$)($n$2).($b$)[$ Select $]$ If f$($n$)$ O$($n$)$ and g$($n$)$ O$($n$2),$ then n $\backslash$times f$($n$)+$ g$($n$)($n$2).($c$)[$ Select $]$ If f$($n$)$ O$($n$),$ then n $\backslash$times f$($n$)+2000$n $($n$2).($d$)[$ Select $]$ If f$($n$)$ O$($n$),$ then n $\backslash$times f$($n$)+2000$n$2($n$2).($e$)[$ Select $]$ n$!$ O$(2$n$).$