QUESTION $1[$Total marks: $10]$ Regular Expressions & DFAs $1($a$)[4$ Marks$]$ Given a binary alphabet $\{0,1\},$ write a regular expression that recognises all words that have an odd number of $1$s and end with a $1.1($b$)[6$ Marks$]$ Use the subset construction method to derive a deterministic finite state automaton $($via a nondeterministic finite state automaton$)$ that recognises the language from part $($a$).$