 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/discrete-mathematics-continuous-mathematics-and-probability/1/b/i/solution

\overline{A} \oplus \overline{B} = (\overline{A} \cap B) \cup (\overline{B} \cap A) = (B ∖ A) \cup (A ∖ B) = A \oplus B .

Interchanging the two sets simply interchanges the two terms of this union, whose commutativity gives

\overline{A} \oplus \overline{B} = A \oplus B, A \oplus B = B \oplus A .

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