Prove the following statements about languages.

$($a$)[5$ marks$]$ Consider the language specified by the regular expression $[$A$-$Z$][0-9][$A$-$Z$][0-9][$A$-$Z$][0-9].$

Is this language finite or infinite? Prove your answer.

$($b$)$ Consider the language specified by the regular expression $(110*)*.$

i$.[5$ marks$]$ Prove that this language contains words consisting of only $1$s$.$

ii$.[5$ marks$]$ Prove that this language does not contain words that have exactly three $1$s in

a row $($i$.$e$.$ does not start with $1110,$ does not end with $0111,$ and does not have $01110$ as a

substring$)$