Given a context$-$free grammar:

$<$ expr $>-><$ expr $>+<$ term $>|<$ expr $>-<$ term $>|<$ term $>$

$<$ term $>-><$ term $>*<$ factor $>|<$ term $>/<$ factor $>|<$ factor $>$

$<$ factor $>-><$ expr $>|<$ digit $>$

$<$ digit $>->0|1|2|3|4|5|6|7|8|9$

$($a$)(4$ pts$)$ If possible show the leftmost and rightmost derivation parse tree for the

given expression:

$8/4-2+1$

$($b$)(3$ pts$)$ Using the rules to convert Parse Tree to Abstract Syntax tree $($AST$)$

convert the rightmost derivation parse tree generated in part$($a$)$ to AST.

$2.(3$ pts$)$ Given regex $($a$|$b$)$a$($a$|$b$)*($a$|$b$),$ generate a context$-$free grammar for the same.