Let $L$ and $L'$ be languages over the alphabet $\Sigma $. The left quotient of $L$ by $L'$ is
$L/L'\overset{{def}}{=} \left\{w \in \Sigma^* : wx ∈ L\text{ for some }x \in L'\right\}$
Which of the following is true?
- If $L/L'$ is regular then $L'$ is regular.
- If $L$ is regular then $L/L'$ is regular.
- If $L/L'$ is regular then $L$ is regular.
- $L/L'$ is a subset of $L$.
- If $L/L'$ and $L'$ are regular, then $L$ is regular.