$1\mathrm{.}8$ Use the construction in the proof of Theorem $1\mathrm{.}45$ to give the state diagrams of

NFAs recognizing the union of the languages described in

a$.$ Exercises $1\mathrm{.}6$a and $1\mathrm{.}6b.$

b$.$ Exercises $1\mathrm{.}6c$ and $1\mathrm{.}6f.$

THEOREM $1\mathrm{.}45$

The class of regular languages is closed under the union operation.

$1\mathrm{.}6$ Give state diagrams of DFAs recognizing the following languages. In all parts, the

alphabet is $\{0,1\}.$

a$.$ begins with a $1$ and ends with a $0$