$8$ Problem $8$:

Consider the following languages $A,B,$ and $C$ defined over the alphabet $=$

$\{x,y\}$ :

$A=x{y}^{+}yx$

$B=x(yy{)}^{+}yx$

$C=x(yy{)}^{**}x$

Answer each of the following questions considering the definition above.

a$)$ Give an example string that is accepted by all three languages.

b$)$ Give an example string that is accepted by only $A.$

c$)$ Give an example string that is accepted by only A and B$.$

d$)$ Give an example string that is accepted by only A and $C.$

e$)$ Give an example string that is accepted by only C$.$

f$)$ Indicate if there is a subset$/$superset relation between any pair of the three

languages.