I want to prove that the following language is decidable:
$$\mathit{SEQ}_{\mathit{CFG}} = \{⟨G⟩ \mid \text{$G$ is CFG and $L(G) ⊈ L$}\}, \text{ where } L = \Sigma^* - \{\epsilon\}$$
So, I think about the relationship between equality and substrings.
for example, I saw in different questions that when we have $L(G) = L(H)$ we can perform that proof on the $L(G) ⊆ L(H)$.
So can I do that with $L(G) ⊈ L$?
So what is the benefit of saying $L = \Sigma^* - {\epsilon}$ ? I'm a bit confused. Can anyone help me with this question?