Let $L_1$ be a regular language, $L_2$ be a deterministic context-free language and $L_3$ a recursively enumerable, but not recursive, language. Which one of the following statements is false?
- $L_1 \cap L_2$ is a deterministic CFL
- $L_3 \cap L_1$ is recursive
- $L_1 \cup L_2$ is context free
- $L_1 \cap L_2 \cap L_3$ is recursively enumerable
My attempt :
- False, Since $\text{DCFLs are not closed under union nor intersection}$.
- False, that should be recursive enumerable but not recursive.
- True.
- True.
Can you explain for option $(1)$, is DCFL are closed under Intersection with Regular Languages?
Somewhere, it explained as $\text{DCFL are closed under Intersection with Regular Languages}$.