Let R $=($ba$$

b $+$ aba$$

ba$)$

$$ and S $=($a

$$

ba$$

ba$$

$)$

$$

$,$ both over $\backslash$Sigma $=\{$a$,$ b$\}.$

$($a$)$ Give an example of a string z that is both in R and in S $($that is$,$ z in R $\backslash$cap S $).$

$($b$)$ Is it possible to find a string x that is in R and is not in S $($that is$,$ x in R $\backslash$cap S$)?$ If yes,

write it down; if not explain briefly why.

$($c$)$ Is it possible to find a string y that is in S and is not in R $($that is$,$ y in S $\backslash$cap R$)?$ If yes,

write it down; if not explain briefly why.