6. Let L1 and L2 be two languages. (a) Define the exclusive-or (XOR) operation as L1La = {xl either x L1 or x L2 but not both) Prove or disprove that Turing-recognizable languages are closed under the XOR operation. Answer: (b) Define the divide operator as L/L2-(al L1 for some y L2} To illustrate the divide operator, suppose that Li = {w is a palindrome) and that L2 -[w w has even number of a's and b's]. Since aababbbabaa E L1 and bbabaa E L2 then aabab E 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 L1La = {xl either x L1 or x L2 but not both) Prove or disprove that Turing-recognizable languages are closed under the XOR operation. Answer: (b) Define the divide operator as L/L2-(al L1 for some y L2} To illustrate the divide operator, suppose that Li = {w is a palindrome) and that L2 -[w w has even number of a's and b's]. Since aababbbabaa E L1 and bbabaa E L2 then aabab E L1/L2 because aabab +bbabaa - aababbbabaa Prove or disprove that Turing-recognizable languages are closed under the divide operation