With the following definition having been given:

Let

$p(n)={\displaystyle \underset{i=0}{\overset{d}{}}}{a}_i{n}^i,$

where $a_d>0,$ be a degree$-d$ polynomial in $n,$ and let $k$ be a constant.

Which of the following "propositions" are valid?

a$.$ If $kd,$ then $p(n)=O(n^k).$

b$.$ If $kd,$ then $p(n)=(n^k).$

c$.$ If $k=d,$ then $p(n)=(n^k).$

None of the propositions are valid.

All of them are valid $($i$.$e$.,$ a$.,$ b$.,$ and c$.).$

Only $a.$ is valid.

Only $c.$ is valid.

Only $b.$ is valid.