(DFA Construction: Addition Verification) Let sigma_2 = {0, 1}, and define sigma = sigma^3_2. Informally, sigma is the set of triples of the form (a, b, c) where a, b, c are single binary digits. Consider a string s elementof sigma^it is a sequence of such triples. We want to "verify" binary addition of numbers in the first two coordinates by checking that it is equal to the third. Let A be the language of such triples such that the concatenation of the first coordinates, as a number and the concatenation of the second coordinates, as a number, sum to be equal to the third. For example, if w = (0, 1, 1)(1, 1, 1)(0, 0, 1) (1, 0, 1), this is encoding 0101_2 + 1100_2 = 1111_2, which is false: therefore, w A. Prove that A is regular