If $L_{1} \subseteq L_{2}$ and $ L_{2}$ is regular, does it follow that $L_{1}$ is necessarily regular? I don't understand this question, is there any proof to show this or is there an assumption we make?
Regular language subsets
regular languages;regular expressions;sets
No, $L_1$ is not necessarily regular. We could have $L_2 = \Sigma^*$, in which case $L_1$ could be anything at all.