Question $5$

$10$ pts

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$)$ If $f(n)inO(n^2)$ and $g(n)in(n),$ then $f(n)+ng(n)in(n^2)$

$($b$)$ If $f(n)inO(n)$ and $g(n)inO(n^2),$ then $nf(n)+g(n)in(n^2)$

$($c$)$ If $f(n)inO(n),$ then $nf(n)+2000$nin$(n^2).$

$($d$)$ If $f(n)inO(n),$ then $nf(n)+2000n^{2}in(n^2).$

$($e$)n!$inO$(2^n).$