Problem $3(30$ points$)$ For parts $($a$)-($e$),$ decide if it is true or false. If the statement

is true, then prove it $($to prove it you will either need to use the definition and find

constants or use the limit laws$).$ If the statement is false, then give a reason or a

counterexample. Then answer part $($f$).$

$8n^3=O(n^4).$

$n^{3}in(n^4)$

$2^n$inO$(2^{n+1})$

$n!in((n+1)!)$

What does $O(1)$ mean?

What does $(1)$ mean?