Please write the answers clear and easy to be read and please sipirt the answers so It would be in order Problem 1 (5 points). Consider the set S-{ : c NU {0},de Q, d 0}. Prove that Problem 2 (5 points). Assuming the alphabet is 10, 1), build a DFA that recognizes the following la: he leglh ow,ivible by 3J. No: mpty axing, h length 0, which is divisible by 3. Problem 3 (5 points). Assuming the alphabet is 0, 1), build a DFA that recognizes the following language: {w: w ends with the sequence 10). Problem 4 (5 points). Succinctly describe the language of the following DFA: 0, 1 0 0 0, 1