= Solution
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> satisfies
$$
A\oplus\mathcal U=(A\setminus\mathcal U)\cup(\mathcal U\setminus A)=\varnothing\cup\overline A=\boxed{\overline A}.
$$
The <disjoint sets> $A$ and $\overline A$ have <union> $\mathcal U$, so
$$
A\oplus\overline A=(A\setminus\overline A)\cup(\overline A\setminus A)=A\cup\overline A=\boxed{\mathcal U}.
$$
Back to article page
