$(15$ points$)$ Suppose language $L_2$ consists of mathematical expressions that has terminals $0-9$ and $,,+\frac{-}{,}**.$ Assume that the minimum value in an expression is $0$ and the maximum value is $9,$ that is the expression $11-5$ would not be possible but the expression $6+9$ would be possible.

Some sample expressions in the proper syntax include $4,6+9,2-3+4.$ Expressions such at $5**+3$ would not be$.$

Do one of the following:

$($a$)$ Construct a context$-$free grammar for $L_2.$ Use $S$ as the start symbol and give the $4-$tuple.

$($b$)$ Construct a pda for the language and give the septuple $($transition functions are not needed for this one$).$