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 Incoming links: Double negation

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 2026-10-31

Using set difference as an intersection with a complement of a set, and using double negation, gives

\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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