Given the following two statements:
$S_1$: If $L_1$ and $L_2$ are recursively enumerable languages over $\Sigma^*$, then $L_1 \cup L_2$ and $L_1 \cap L_2$ are also recursively enumerable.
$S_2$: The set of recursively enumerable languages is countable.
Which of the following is true?
- $S_1$ is correct and $S_2$ is not correct
- $S_1$ is not correct and $S_2$ is correct
- Both $S_1$ and $S_2$ are not correct
- Both $S_1$ and $S_2$ are correct