Chapter 7.3, Problem 8ES

Let S be the set of all strings in a’s and b’s and let $L:S\to \text{Z}$ be the length function:

For all strings $s\in S$ , $L\left(s\right)=$ the number of characters in s. Let $T:\text{Z}\to \left\{0,1,2\right\}$ be the mod 3 function:

For every integer n, $T\left(n\right)=nmod3$ .

a. $\left(T\circ L\right)\left(abaa\right)=?$

b. $\left(T\circ L\right)\left(baaab\right)=?$

c. $\left(T\circ L\right)\left(aaa\right)=?$