$($d$)$ Consider the finite automaton with states $\{A,B,C\},$ alphabet $\{1,2,3\},$ one starting

state A$,$ one final state B$,$ and transitions embodied in the diagram below. Answer the

following questions with reference to this automaton.

$[8$ marks$]$

i$.$ Is this a non$-$deterministic finite automaton? Why?

ii$.,$ Which of these words are accepted by the automaton: $121,112,122,11.$

iii. How is the word $121$ processed by the automaton?

iv$.$ How should you modify the automaton so that only the empty word is

added to the language generated by the automaton, and no other changes

occur to the original language?

v$.$ Does removing state $C$ and associated transitions affect the language

represented by the automaton? Why?