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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?

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    $\begingroup$ Please do not vandalize your question. $\endgroup$ – ArtOfCode Aug 10 '16 at 12:49
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No, $L_1$ is not necessarily regular. We could have $L_2 = \Sigma^*$, in which case $L_1$ could be anything at all.

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