Consider the complexity class $CO-NP$ as the set of languages $L$ such that $\overline{L}\in NP$, and the following two statements:

$S_1: P\subseteq CO-NP$

$S_2:$ If $NP\ne CO-NP$, then $P\ne NP$

Which of the following is/are correct?

Statement $S_1$ is true.

Class $P$ is closed under complement. Also, $P\subseteq NP$.

So,

$P\subseteq CO-NP$

Statement $S_2$ is also true.

If $P=NP$, then since $P$ is closed under complement, we would get

$NP=CO-NP$

But the statement says $NP\ne CO-NP$.

Therefore, $P\ne NP$.

Hence, both $S_1$ and $S_2$ are correct.