In all of the regular languages below we are using alphabet $\{A,B\}$ for both automata and regular expressions. All words and transitions must be made using only these two letters and $lon.$

$($a$)$ Consider the regular expression $(BA|).$ Which of the following words belong to the language of this regular expression and which ones do not: $lon,$AAA,ABB,AAAB,$BBBB,$BABAA,BABAB,ABBAAB

$($b$)$ Take the regular expression: $(BA|)$ and convert it into an NFA Draw this $($b$).$ Show all working mathematically