I. (10 points). The alphabet for this question is ?-(0,1). Consider the following sets. Fill in each blank below with A1, A2, or A3 to make the statement true, or write "None of the above" if none of these sets do. (If multiple choices work, you only need to give one of them for full credit.) a. DOUBLE b. DOUBLEis nonregular. c. STUTTER is regular d. STUTTER is nonregular. e. STUTTER ) is regular. The definitions for these operations are the same we've worked with before: For L a set of strings, we can define the following associated sets DOUBLE(L) = {vu | u E L} Note: ? is in each of these sets iff it is an element of L itself. No justifications required for credit for this question; but, as always, they're a good idea for your own benefit. Extension (not for credit): Do any of the examples you saw above prove whether the statement "The class of regular languages is closed under DOUBLE" is true or false? How about whether the statement "The class of nonregular languages is closed under DOUBLE" is true or false