Chapter 1.3, Problem 12ES

Let $A=\left\{x,y\right\}$ and let S be the set all strings over A. Define a relation C from S to S as follows: For all strings s and t in S,

$\left(s,t\right)\in C\text{means}\text{that }t\text{=}\text{ys}$

Then C is a function because every string in S consists entirely of x’s and y’s and adding an additional y on the left creates a single new string that consists of x’s and y’s and is, therefore, also in S. Find C(x) and C(yyxyx).