Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability / 1 / b

Use the definition $A\oplus B=(A\setminus B)\cup (B\setminus A)$ of symmetric difference. The algebraic laws for set difference and the empty set giveand

Because $A\subseteq \mathcal{U}$, the set difference $A\setminus \mathcal{U}$ is empty and $\mathcal{U}\setminus A=\overline{A}$. Therefore the symmetric difference satisfiesThe disjoint sets $A$ and $\overline{A}$ have union $\mathcal{U}$, so