Given $A,B$ regular languages. Prove the existence of $C\in L_{regular}$ so that: $A \prec C \prec B $
Whereas $A\prec B$ stands for: $A\subset B $ and $B\setminus A $ is infinite regular language.
I tried to go for: $C=\overline{B} \cup A$ and some other options but it didn't work out.
EDIT: It is also given that: $A\prec B$.
The problem statement is not clear, but I assume $A≺B$, So $D=B-A$ is an infinite regular language. Now as shown here, $D$ can be written as $D=L_1\cup L_2$, where $L_1$ and $L_2$ are infinite regular languages and $L_1 \cap L_2=\varnothing$. Consider $C=A \cup L_1$.