$1$ Straightforward

$75$

Consider the following grammars:

$4**2+2+4+2=16$

$($a$)$ Check if the following strings belong to $L(G_1)$ and$/$or $L(G_2).$ If a string belongs to a language, show its derivation. If a string does not belong to a language, justify.

i$.abc$

ii$.$ aabccc

iii. aacc

iv$.$ abbc

$($b$)$ Reason if $G_1$ and $G_2$ are regular grammars according to Chomsky's Hierarchy.

$($c$)$ Show that $L(G_1)=L(G_2).$

$($d$)$ Is $L(G_2)$ a regular language?