2. Let A = {0} and B = {1}. For n > 1, recursively define An=(An-1...

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2. Let A = {0} and B = {1}. For n > 1, recursively define An=(An-1 {0}) (Bn-1 {1}) B = (An-1 {1}) (B-1 {0}). (a) List the elements in A3 in lexicographical order, and list the elements in B3 in lexico- graphical order. Justify. (b) Give a characterization of the elements in A, for arbitrary n 1 in plain English. Explain. 2. Let A = {0} and B = {1}. For n > 1, recursively define An=(An-1 {0}) (Bn-1 {1}) B = (An-1 {1}) (B-1 {0}). (a) List the elements in A3 in lexicographical order, and list the elements in B3 in lexico- graphical order. Justify. (b) Give a characterization of the elements in A, for arbitrary n 1 in plain English. Explain.