Problem $17($Homework $2$ Problem $5).$ Let $$ be a finile alphabel and let $L_0,L_1$sube${}^{**}$ be languages

such that $L_0{L}_1=$empty set. Think of $L_0$ and $L_1$ as the sets of "bad" and "good" strings respectively. We wish

Lo design an aulomaton which is guaranteed to reject every string in $L_0$ and accept every string in $L_1.$ Our

aulomaton is allowed to behave arbilrarily on strings that are neilher in $L_0$ nor in $L_1.$ In other words, our

aulomaton is required to recognize some language Lsube${}^{**}$ such that $L{L}_0=\frac{O}{?}$ and $Lsupe{L}_1.$

For concreleness, let us say that we are looking for a DFA over the alphabet $=\{0,1\}.$ Also, let

$L_0=\{\begin{array}{ccc}\text{x}\text{i}\text{n}& \{0,& 1{\}}^{**}|\end{array}$ the number of $0^{\text{'}}\text{'}$s and $1\text{'}$s in $x$ are unequal