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

NFAs recognizing the union of t

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

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

a$.\{$w$|$w begins with a $1$ and ends with a $0\}$

b$.\{$w$|$w contains at least three $1$s$\}$