Suppose $$ is alphabet and ${}^{**}$ is the set of strings over $,$ defined recursively $($check lecture

for definition$).$ Consider the function $R$:${}^{**}{}^{**}$ which reverses a string, e$.$g$.,$

$R(01001)=10010.$

Give a recursive definition for $R.($Your recursive definition should mirror the structure of

the recursive definition of ${}^{**}.)$

The definition: We can define functions on recursively defined sets using basis$/$rec$.$ rule.

Define a function l : $\backslash$Sigma $-->$ N that gives the length of a string in $\backslash$Sigma $.$

$$ Basis: l$()=0,$

$$ Rec. rule: l$($wx$)=$ l$($w$)+1$