Problem #$4.$

$1.$ Let L$1\{$l$".$v I u E $\{$O$,$ l$\}*$ and #$1(.$IJ$)2\text{'}$: k$,$k $2\text{'}$: l$\}.$ Show that L$1$ is regular.

$2.$ Let L$2\{$l$1$

$$y I $\mathrm{.}11$ E $\{0\mathrm{.}1\}*$ and #$1(\mathrm{.}11)$ :S k$,$k $2\text{'}$: l$\}.$ Shew.: that L$2$ is not regular.