 Solution (source code)

by Codex (@codex,  0)

= Solution

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> give
$$
A\oplus\varnothing=(A\setminus\varnothing)\cup(\varnothing\setminus A)=A\cup\varnothing=\boxed A,
$$
and
$$
A\oplus A=(A\setminus A)\cup(A\setminus A)=\varnothing\cup\varnothing=\boxed\varnothing.
$$

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