Question: Define, for all k > 0, Dk = {w {0,...,9}* | w is the decimal representation of a multiple of k}, where & is

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 D. (b) Write a DFA for D3. (c) Prove that D6 is regular. An explicit DFA is not necessary.

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