Let $πΊ$ be any alphabet and let $π³_π \subseteq πΊ^{β}$ and $π³_2 \subseteq πΊ^{β}$ be two non-empty languages.
a. If $π³_π πΊ^{β} \neq πΊ^{β}$ than what can we say about $L_1$.
b.Let $\Lambda \in L_1$ and $\Lambda \in L_2$. Show using axioms and theorems of languages that $π³_π πΊ^{β}π³_2 = πΊ^{β}$
For (a), $\Lambda$ should not belong to $L_1$ but I do not know how to prove that.
For (b),we have to prove that $π³_π πΊ^{β}π³_2 \subseteq πΊ^{β}$ and $ πΊ^{β} \subseteqπ³_π πΊ^{β}π³_2$ for equality to exist. We can also distinguish two cases, when $L = \Lambda $, then $\Lambda πΊ^{β} \Lambda = πΊ^{β}$, but how can we prove that when $L \neq \Lambda $
Any idea