$($III$)$ Consider the grammars G$1$ and G$2$ above. Show that L$1$ L$2$ is context free

by constructing a complete grammar.

$($i$)$ Derive any string w$1$ that belongs to L$1$ and any string w$2$ that belongs

to L$2.$

$($ii$)$ Show that w$1$ w$2$ that belongs to L$1$ L$2$

$($IV$)$ Consider the grammars G$1$ above. Show that L$1*$ is context free by

constructing a complete grammar.

$($V$)$ Name two closure properties that are true for regular languages that are

not necessarily true for CFL$.$