Show that the following language over the alphabet $=\{0,1\}$ is regular:

$D=\{w|w$ contains $an$ equal number $of$ occurrences $of$ the substrings $01$ and $10\}$

Note that $1011001$inD because it contains two occurrences each of $01$ and $10$ as substrings.

On the other hand, $10110!$inD because $10110$ contains two occurrences of $10$ and one occur$-$

rence of $01.(8$ points$)$

Note that the regularity of $D$ contrasts with the nonregularity shown in the textbook and

class of the language

$C=\{w|w$ contains $an$ equal number $of0\text{'}s$ and $1\text{'}s\}$