Given the following dangling else grammar:

$(1$a$)$ S $->$ if b then S X

$(1$b$)$ S $->$ o

$(2$a$)$ X $->$ epsilon

$(2$b$)$ X $->$ else S

where terminal b stands for any boolean expression and terminal o stands for any other statement.

$($a$)$ Augment the grammar with a rule that includes the end of file symbol and produce NULLABLE, FIRST, and FOLLOW sets for each of the nonterminals.

$($b$)$ Produce the predictive parsing table. There will be a slot with with multiple entries $($X $->$ else S and X $->$ epsilon$).$ Remove the X $->$ epsilon entry.

$($c$)$ Show the parse trees obtained by predictive parsing

$($c$\mathrm{.}1)$ if b then o else if b then o else o $ and

$($c$\mathrm{.}2)$ if b then if b then o else o $$.$

solve this question by hand on paper. please define each step briefly.