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

L$0=\{$x in $\{0,1\}|$ the number of $0$s and $1$s in x are unequal$\}$ and L$1=\{0$n$1$n $|$ n in N $\backslash$cup $\{0\}\}.$ Observe

that L$0\backslash$cap L$1=.$ Does there exist such a DFA which accepts every string in L$1$ and rejects every string in

L$0?$ Prove your answe