\exercise{}{0}
\solution
\textcolor{blue}{
    The syntax of regular expressions given by Definition 3.13 is the following:
    \begin{enumerate}
        \item The constants $\epsilon$ and $\varnothing$ are regular expressions, with L($\epsilon$) = {$\epsilon$} and L($\varnothing$) = $\varnothing$.
        \item For each $a\in\Sigma$, \textbf{a} is a regular expression, with $L(a)=\{a\}$.
        \item If E and F are regular expressions, then (E+F) is a regular expression with $L((E+F))=L(E)\cup L(F)$.
        \item If E and F are regular expressions, then (EF) is a regular expression with $L((EF))=L(E)L(F)$.
        \item If E is a regular expression, then $(E^*)$ is a regular expression, with $L((E^*))=(L(E))^*$.
    \end{enumerate}
    So let us denote a grammar $G=(V,T,P,S)$, where $V={S}$ and T is T from the problem statement, we have the following P:\\ \\
    \begin{center}
        $\text{S}\rightarrow\varnothing|\epsilon\leftarrow$for rule 1\\
        $\text{S}\rightarrow \text{a}|\text{b}\leftarrow$for rule 2\\
        $\text{S}\rightarrow\text{S}+\text{S}\leftarrow$for rule 3\\
        $\text{S}\rightarrow\text{SS}\leftarrow$for rule 4\\
        $\text{S}\rightarrow\text{S}^*\leftarrow$for rule 5\\
    \end{center}
}

\exercise{}{0}
\solution
\textcolor{blue}{
    Let us denote the grammar $G=(V,T,P,A)$ where:
    \begin{align*}
        V&=\{A,B\}\\
        T&=\{1,0,\epsilon\}
    \end{align*}
    \begin{align*}
        P: &A\rightarrow 0A|1B|\epsilon\\
        &B\rightarrow 0A|\epsilon\\
    \end{align*}
}