Let $W$ be the sit of all five$-$letter $5$ trings over the alphabet $=\{a,b,$dots,$z\}$ and let $D$ be a arbitrary subset of $W.$ We define the language $C_D$ to be the set of all strings that contain five consecutive letters that form a string in $D.$

a$)$ Prove, by any method, that for any $D,$ the language $C_D$ is regular

b$)$ Prove a finime upper bound on the number of Myhill$-$Nerode classes in $C_D$ for any $D.$

c$)$ Prove that for any $D$ with $|D|=n,$ there are at most $5n+1$ My clas for $C_D.$