Let Cn={w{0,1,2}w is a number in base 3 that is a multiple of n} . For example, 2210C2 but 2210C3 , since 2210 in base 3 is 75 in base 10. Give a DFA for C2 . Show that for all n , Cn is regular by giving a DFA for it. Hints: As in Exercise 2, you must specify the DFA as a 5-tuple that depends on n . You need only remember the current value of the number modulo n . Reading a 1 changes the current value from K to 3K+1 . If K is some integer and k is its value modulo n , then 3K+1 is congruent to 3k+1 modulo n