I have following statements which I must prove or disprove :1) Let $L$ be a CFL and $k \in N$ then $L^k$ is also a CFL.2) $L_1 \subseteq L_2 \subseteq L_3$  are Languages, if $L_1$ and $L_3$ are DCFL, then $L_2$ is also a DCFLThe first one I have no idea how to start or whether it is also a CFLFor the second one I think that this is false, because the CF contains the REG and DCF which means $L_2$ can be a REG-Language or a CFL or DCFL?Is this right? at least this is how I understand it
CFL Closure Properties prove or disprove for the following languages
formal languages;context free;closure properties
1) Since the context-free languages are closed under concatenation, a simple induction shows that if $L$ is context-free then so is $L^k$, for all $k \geq 0$.2) Let $L_2$ be a language over an alphabet $\Sigma$ which is not context-free. Then $\emptyset \subseteq L_2 \subseteq \Sigma^*$, refuting the statement (since $\emptyset$ and $\Sigma^*$ are regular and so deterministic context-free).