6. Let L1 and L2 be two languages. (a) Define the exclusive-or (XOR) operation as L12 = {xl either x E L1 or x L2 but not both} operation. Prove or disprove that Turing-recognizable languages are closed under the XOR Answer: (b) Define the divide operator as L1/L2 ry E L1 for some y E L2) To illustrate the divide operator, suppose that Li-ful w is a palindrome} and that L2 w has even number of a's and b's. Since aababbbabaa E L1 and bbabaa E L2 then aabab L1/L2 because aabab + bbabaa-> aababbbabaa. Prove or disprove that Turing-recognizable languages are closed under the divide operation. Answer: 6. Let L1 and L2 be two languages. (a) Define the exclusive-or (XOR) operation as L12 = {xl either x E L1 or x L2 but not both} operation. Prove or disprove that Turing-recognizable languages are closed under the XOR Answer: (b) Define the divide operator as L1/L2 ry E L1 for some y E L2) To illustrate the divide operator, suppose that Li-ful w is a palindrome} and that L2 w has even number of a's and b's. Since aababbbabaa E L1 and bbabaa E L2 then aabab L1/L2 because aabab + bbabaa-> aababbbabaa. Prove or disprove that Turing-recognizable languages are closed under the divide operation