$2.$Use the general algorithm that we learned in class to design a non$-$deterministic finite automaton that recognizes the language $($a U A U r$)*($a U A$)$ of all the words that end with small or capital A and contain only letters a$,$ A$,$ and r:

a$,$ A$,$ and r are languages consisting of only one $1-$symbol word each: a is a language consisting of a single $1-$symbol word a; r is a language consisting of a single $1-$symbol word r$,$ etc.;

for any two languages C and D$,$ the notation CD means concatenation;

transform the resulting non$-$deterministic finite automaton into a deterministic one$\mathrm{.}2.$