Explain this one ?

Question

L1={ϕ}

L2={ Σ *}

My question is how  L1 is a subset of L2  but not the proper subset ?

also how L1 is a subset of L2 ??  explain ?

Answer 1

Here $L_1 = \{\{\}\}$ is a set of sets and not a set of strings and hence is not a language.

Suppose $L_1 = \{ \epsilon\}$,

Now, all strings (only 1) in $L_1$ is present in $L_2$. Is there anyother string in $L_2$ - yes, if $\Sigma$ is non-empty. So, if $\Sigma$ is non empty, then $L_1$ is a proper subset of $L_2.$

Comments

Thnks Arjun Sir for your explanation as always.