Eliminate the variable B from the grammar

S $$ aSB $|$ bB$,$

B $$ aA $|$ b

$2.(15$pts$)$ Show that the two grammars

S $$ abAB $|$ ba$,$

A $$ aaa,

B $$ aA $|$ bb

and

S $$ abAaA $|$ abAbb $|$ ba$,$

A $$ aaa

are equivalent.

$3.(15$pts$)$ Eliminate all useless productions from the grammar

S $$ aS $|$ AB $|,$

A $$ bA$,$

B $$ AA

What language does this grammar generate?

$4.(15$pts$)$ Eliminate all $-$productions from

S $$ AaB $|$ aaB,

A $,$

B $$ bbA $|$