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). Assuming the alphabet is 10, 1], prove that the following language is regular: w : w ends with an odd number of 1's) Problem 2 (5 points). Assuming the alphabet is 10, 13, prove that the following language is regular: {w : w does not end with a 0) Problem 3 (5 points). Show the DFA produced by the construction process detailed in class to build the DFA for the following language: fw: w contains an odd number of 1's U {w : w does not end with a 0. Do not simplify the DFA, show what the process builds. Problem 4 (5 points). Assuming the alphabet is [0, 1], build an NFA that recognizes the following language: wv : w ends with an odd number of 1's and v does not end with a 0)