$1$ Even or Odd

Let $A=\{a,b\}.$

a$)$ Define, by structural induction, a function

$f$:$A^{**}$ Bool

that determines, for an input word $win{A}^{**},$ if the letter a occurs an even number

of times in $w.$ For example, we should have $f(babba)=$ true and $f(abbaa)=$ false.

Note: Bool is the set true, false