$1.[15$ marks$]$ Briefly describe, in one short sentence, the languages denoted by the following regular expressions over the alphabet $\{$a$,$ b$\}.($The first one is already solved as an example.$)$

a$)$ a$($a$|$b$)*$a

Answer: All strings that begin and end with the symbol a$.$

b$)($a$|$b$)*$a$($a$|$b$)($a$|$b$)$

c$)$ a$*$ba$*$ba$*$ba$*$

d$)($a$*$ba$*$b$)*$a$*$