Q $1.$Let L be any language over an alphabet $\backslash$Sigma $.$ Prove or disprove L$^+$ is finite only if L $=..$

Q $2.$Draw a DFA for the language over input alphabets $\backslash$Sigma $=\{0,1\}$ that accepts

strings a$)$ starting with $`1\text{'},$ b$)$ ending with $10,$ c$)$ starting with $1$ and ending with $10.$

Q $3.$Let $\backslash$Sigma $=\{0,1\}.$ For each of the following languages design a DFA with

minimal number of states that accept the language.

i$)$ Draw a DFA that accepts the string $10$ or $010.$

ii$)$ Draw a DFA that accepts all strings but $001$