#### Question

For each of the following languages, give two strings that are members and two strings that are not members-a total of four strings for each part. Assume the alphabet $\Sigma=\{\mathrm{a}, \mathrm{b}\}$ in all parts. a. $\mathrm{a}^{*} \mathrm{b}^{*}$, b. $\mathrm{a}(\mathrm{ba})^{*} \mathrm{b}$, c. $a^{*} \cup b^{*}$, d. $\mathrm { (aaa)^* }$, e. $\Sigma^{*} a \Sigma^{*} b \Sigma^{*} a \Sigma^{*}$, f. $\mathrm { aba \cup bab }$, g. $(\varepsilon \cup \mathbf{a}) \mathbf{b}$, h. $(\mathrm{a} \cup \mathrm{ba} \cup \mathrm{bb}) \Sigma^{*}$.

#### Solution

Verified#### Step 1

1 of 9$\boxed{\textbf{Part a.}}$

In strings in this language all $\texttt{a}$'s (possibly none) come before all $\texttt{b}$'s (possibly none).

Members: $\texttt{b}, \texttt{aaabb}$

Not members: $\texttt{abba}, \texttt{ba}$