Problem $7.$ For each language below, use the pumping lemma $($page $78)$ to

prove that it is not regular:

b$)L_2=\{\begin{array}{cc}w|win\{1,& \text{\#}{\}}^{**}\end{array}$ and $w=x_1$#$x_2$#dots#$x_k$ for $k0,$ each $x_{i}in{1}^{**},$

and $x_i{x}_j$ for $\{$:$ij\}.$