Given a formal language L, is $L \subset L^*$ or is $L \subseteq L^*$?
To give context, I am tasked with proving whether or not there exists a language such that $(L^*)^c = (L^c)^*$. Assuming the logic behind my proof is correct, I've concluded that if $L \neq L^*$ then $(L^*)^c$ cannot equal $(L^c)^*$. I won't go into my proof as it's the not primary subject of my question (that is, unless someone is interested enough to check my work).
Thanks for any assistance!
Both are possible. For example, we have $\{a\}\subsetneq \{a\}^*$, but $\{a^n\mid n\ge 0\}=\{a^n\mid n\ge 0\}^*$.
For your "contextual" question, consider $L=\varnothing$...