Constructing Grammars

$($a$)$ Let $=\{a,b,+,,(),{?}^{**}\}.$ Define Lsube${}^{**}$ to be the set of all syntactically legal

regular expressions over the alphabet $\{a,b\}.$ Construct an umabiguous context$-$free

grammar $G$ that generates $L.$ Your grammar should create parse trees that correspond

to assigning the following precedence levels to the operators $($from highest to lowest$)$:

Kleene$-$star $*,$ concatenation, union $+.$

$($b$)$ Show the parse tree that your grammar will produce for the string $(a+b)b{a}^{**}.$