Theory of computing - thanks so much in advance!

1. Designing finite automata Define, for all k>0, Dk={w{0,,9}w is the decimal representation of a multiple of k}, where is considered to represent the number 0 . For example, the strings , 0,88 , and 088 all belong to D2, but 99 and 099 do not. (a) Write a DFA D2. (b) Write a DFA for D3. (c) Prove that D6 is regular. An explicit DFA is not necessary