Problem $1$: Consider the following languages $L_1=\{b,a\},L_2=\{ba,ac,cb\}$ and $L_3=\{bc,ca\},$

from alphabet $\{a,b,c\}$

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 $L=\{b^{2p}{a}^t,p,t0\}($if you think there are no

such strings then state it clearly and explain why$)$

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

Let $=\{b,c\},L_1=\{b\}$ and $L_2=\{c\},$ list all strings of length $2$ that are not from $L_1^{*}{L}_2^{*}($if

you think there are no such strings then state clearly and explain why$)$

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

you think there are no such strings then state clearly and explain why$)$

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

there are no such strings then explain why$)$

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

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

Let $=\{a,b\},L=\{a^n{b}^n{a}^m|n,m0\}.$ List $3$ strings of length $5$ that are not from $L^{*}$