Consider the complexity class $CO-NP$ as the set of languages $L$ such that $\overline{L} \in NP$, and the following two statements:
$S_1: \: P \subseteq CO-NP$
$S_2: \: \text{ If } NP \neq CO-NP, \text{ then } P \neq NP$
Which of the following is/are correct?
- Only $S_1$
- Only $S_2$
- Both $S_1$ and $S_2$
- Neither $S_1$ nor $S_2$