Question $1$

$(1)$ S $->$ aS

$\backslash ($ S$->$S b $\backslash )$

S $->\backslash (\backslash$varepsilon $\backslash )$

$\backslash (\backslash$varepsilon $\backslash ),$ a$,$ b$,$ aa$,$ ab$,$ bb$,$ aaa, aab, abb, bbb and $\backslash (\backslash$boldsymbol$\{$L$\}\backslash )$ is regular

$\backslash (\backslash$varepsilon $\backslash ),$ a$,$ b$,$ aa$,$ ab$,$ bb$,$ aaa, aab, abb, bbb and $\backslash (\backslash$mathbf$\{$L$\}\backslash )$ is not regular

a$,$ b$,$ aa$,$ ab$,$ bb$,$ aaa, aab, abb, bbb$,$ bbba and L is regular

a$,$ b$,$ aa$,$ ab$,$ bb$,$ aaa, aab, abb, bbb$,$ bbba and $\backslash ($ L $\backslash )$ is not regular