Problem $1$: Consider the following languages $L_1=\{0,1\},L_2=\{01,12,20\}$ and $L_3=\{02,21\}$

What is the shortest string $($if there are more than one list all$)$ of $L_2^{+}*(L_3^{**}{L}_1)$

language?

List all strings of length $4$ of $L^{**},$ where $L=\{a^{2m}{b}^n,n,m0\}($if you think there are no

such strings then explain why$)$

List all the elements of $L_1^{+}-L_1^3*L_1^{+}$

Let $L_1=\{a\}$ and $L_2=\{b\},$ list all strings of length $2$ that are not from $L_2^{**}{L}_1^{**}($if you

think there are no such strings then explain why$)$

Let $L_1=\{a\}$ and $L_2=\{b\},$ list all strings of length $3$ that are not from $L_1*L_2^{**}($if you

think there are no such strings then explain why$)$

Let $L_1=\{ab,ba\},$ list all strings of length $4$ that are not from $L_1^{**}($if you think there are

no such strings then explain why$)$

Let $L_1=\{a,b\}$ and $L_2=\{aa,bb\},$ list all strings of length $3$ from $(L_1*L_2{)}^{**}($if you think

there are no such strings then explain why$)$

$L=\{a^n{b}^n{a}^m|n,m0\}.$ List $3$ string that are not from $L^{**}$