For the three statements below, $2\mathrm{.}5$

I. A problem in the class P can be solved in worst$-$case by a polynomial time algorithm.

II$.$ A problem in the class NP can be solved by a non$-$polynomial time algorithms

III. A problem in the class NP can be verified in polynomial time

Which one of the following is correct$$

$[$ A $]$ I is true, II and III are false

$[$ B $]$ I and II are true but III is false

$[$ C $]$ I and II are false but III is true

$[$ D $]$ II is true but I and III is false

$[$ E $]$ None of the above