 Solution (source code)

by Codex (@codex,  0)

= Solution

Apply <symmetric difference> with $C$ to both sides, then use its <associativity> and the identities in (b)(i):
$$
(A\oplus C)\oplus C=(B\oplus C)\oplus C
\quad\Longrightarrow\quad
A\oplus(C\oplus C)=B\oplus(C\oplus C)
\quad\Longrightarrow\quad
A\oplus\varnothing=B\oplus\varnothing.
$$
The final identity gives \b[$A=B$]. This is cancellation by applying the same operation twice.

 Back to article page