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We know that any languages $\subseteq\\\\$ $\Sigma^{*}.$ Because any language collection of string over alphabet. And we know that set of all languages is $2^{\Sigma^{*}}$ which doesn't $\subsetneq\\\\$ $\Sigma^{*}.$ But I have couple of smalls confusion are that

$A.$ Set of all regular languages $\{L_1,L_2,L_3................\}$ is $\subseteq\\\\$ $\Sigma^{*}$ or not?

$B.$ Set of all context free languages $\{L_1,L_2,L_3................\}$ is $\subseteq\\\\$ $\Sigma^{*}$ or not?

$C.$ Set of all recursive enumerable languages $\{L_1,L_2,L_3................\}$ is $\subseteq\\\\$ $\Sigma^{*}$ or not?

$D.$ Any not recursive enumerable language $L$ is $\subseteq\\\\$ $\Sigma^{*}?$

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The set $\Sigma^*$ consists of all words over $\Sigma$.

A language over $\Sigma$ is not a word over $\Sigma$. Hence no language is a member of $\Sigma^*$, and no set of languages is a subset of $\Sigma^*$.

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  • $\begingroup$ "no language is a member of Σ∗" is right but how set of languages is a subset of Σ∗? $\endgroup$
    – Punia
    Oct 8 at 11:55
  • $\begingroup$ Thanks, it was a typo. $\endgroup$ Oct 8 at 12:08
  • $\begingroup$ any not Recursive enumerable language subset of $\Sigma^{*}\$ $\endgroup$
    – Punia
    Oct 8 at 12:17
  • $\begingroup$ any non recursive enumerable language is subset of $\Sigma^*$? $\endgroup$
    – Punia
    Oct 8 at 12:19
  • $\begingroup$ Any language is a subset of $\Sigma^*$, in particular, any non recursively enumerable one. $\endgroup$
    – nir shahar
    Oct 8 at 12:25

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