Actually, I'm wondering if many who got the previous post wrong was because we weren't familiar with the '^' operator. I incorrectly assumed it meant exponentiation.
Granted, not useful in everyday SQL, but the current question is similar to the math behind RAIDed disk. The basic deal is parity is an XOR, P = A^B. If you lose A, then A = P^B = (A^B)^B, and similarly if you lose B.