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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?


marked as duplicate by Ran G., Tom van der Zanden, Evil, D.W. Oct 22 '15 at 21:13

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    $\begingroup$ Please do not vandalize your question. $\endgroup$ – ArtOfCode Aug 10 '16 at 12:49

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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