Please make answers clear and to the point.

Question $1$: Let $=($:$a,b$:$).$ For each of the following Grammars that you see below.

Give one string of size $>0$ generated by the grammar.

Indicate whether the grammar is Regular or not.

If yes, prove that the language generated by the grammar is Regular.

Hint: $a.$ Generate a string of size $>0$

b$.$ Check if the grammar verifies the property of Regular Grammars.

c$.$ If yes Construct the NFA that recognizes $L(G).$

$(1a)G1$: $SaS$

$SSb$

$S$

a$.$ One string of size $>0$ generated by $G1$ is $"$ab$".$

b$.$ Grammar G$1$ is not regular.

c$.$ If yes Construct the NFA that recognizes $L(G1).$