Problem $8$ Let $=\{a,b\}.$

a$.$ Prove that $r=a(a+b{)}^{**}a+b(a+b{)}^{**}b$ is a regular expression using the inductive definition of regular expressions. Use the techniques on slide $9$ in Chap$3\mathrm{.}1$ power point.

b$.$ Give a simple English description of the strings in L$($r$).$

c$.$ Create an NFA $M$ such that $L(r)=L(M).$ Create and test your NFA on Jflap. Submit the jflap diagram for $M$ and the testing diagram for M $.$

d$.$ Testcases: aa$,$ bb$,$ aabb, abbaba, bbaaab, a$,$ b$,$ ababbb, baaababa