Given the following statements:
$S_1$: If $L$ is a regular language then the language $\{uv \mid u \in L, v \in L^R\}$ is also regular.
$S_2$: $L=\{ww^R\}$ is regular language.
Which of the following is true?
- $S_1$ is not correct and $S_2$ is not correct
- $S_1$ is not correct and $S_2$ is correct
- $S_1$ is correct and $S_2$ is not correct
- $S_1$ is correct and $S_2$ is correct