Theorem $4\mathrm{.}1$

If $L_1$ and $L_2$ are regular languages, then so are $L_1{L}_2,L_1{L}_2,L_1{L}_2\frac{,}{b}ar(L_1),$ and $L_1^{**}.$ We say that the

family of regular languages is closed under union, intersection, concatenation, complementation, and

star$-$closure.

Use the construction in Theorem $4\mathrm{.}1$ to find nfa's that accept

$($a$)L((a+b)a^{**})L($baa$*).$

$($b$)L(a{b}^{**}{a}^{**})L(a**b^{**}a).$