Consider the two context$-$free grammars:

G$1$: num $->11|1001|10101|$ num $0|$ num num

G$2$: num $->11|10$ num$01|$ num $0|$ num num

num$->00$ num$|1$ num$|$ e

A$.$ Prove that all strings generated by the two grammars G$1$ and

G$2$ form $($unsigned$)$ binary numbers that are multiples of $3,$ and

examine whether these grammars produce all strings of nonzeros

of multiples of $3$ starting with $1.$

B$.$ Prove that the two grammars G$1$ and G$2$ are ambiguous and transform them into equivalent non$-$ambiguous grammars.

C$.$ Consider whether the two can be converted into equivalent LL$(1)$ grammars by eliminating the features

that make them non$-$LL$(1),$ and then checking for collisions

FIRST$/$FIRST and FIRST$/$FOLLOW$.$

D$.$ For either of the two final grammars in the previous question is not LL$(1),$

see if by looking at a second input symbol you can resolve its conflicts so that the grammar is LL$(2).$