Text Exercise $1\mathrm{.}9.$

Prove that every NFA can be converted to an equivalent one that has a single

accept state.

Text Exercise $1\mathrm{.}10.$a$.$

Show that if $M$ is a DFA that recognizes language $B,$ swapping the accept

and non$-$accept states in $M$ yields a DFA that recognizes the complement to $B.$

Conclude that the class of regular languages is closed under complement.

Text Exercise $1\mathrm{.}15$ selections.

For each of the following languages, give two strings that are members and

two strings that are not members. The alphabet in all cases is $=\{a,b\}.$

a$.a^{*}{b}^{*}$

c$.a^{*}{b}^{*}$

e$.{}^{*}a{}^{*}b{}^{*}a{}^{*}$

g$.(lona)b$