Question $1$

Give a context$-$free grammar for each of the following languages over

$=\{a,b,c\}.$

A$.L1=\{a^m{b}^n{c}^k|n,m0$&$k=3m+2\}$

B$.L2=\{\begin{array}{c}{a}^m{b}^n{c}^k|n=\frac{m}{2}\end{array}$ or $n=k-2$; where $n0,m$ is even &$k2$

Question $2$

Suppose, you are given the grammar below. Now solve the following problems.

$S0S1|1S0|SS|01|10$

A$.$ Show that the grammar is ambiguous by demonstrating three different

parse trees for string $011010.$

B$.$ Find two strings of length six such that those strings do not have more

than one parse tree for the grammar above.