Does a property of Xor like this exist?

Question

Is there a property on Xor that says basically $a = b \oplus (a \oplus b)$? I was thinking associative but I don't think that's correct.

Did you try building a truth table? – Cameron Williams Jul 03 '13 at 05:58 — Cameron Williams, Jul 03 '13 at 05:58
@CameronWilliams No, I haven't learned about those yet. – Jose Jul 03 '13 at 05:59 — Jose, Jul 03 '13 at 05:59

score 4 · Accepted Answer · answered Jul 03 '13 at 05:59

That’s actually a consequence of four properties of $\oplus$: it’s associative, it’s commutative, $x\oplus x=0$ for all $x$, and $0$ is an identity for $\oplus$. The derivation is simple:

$$b\oplus(a\oplus b)=b\oplus(b\oplus a)=(b\oplus b)\oplus a=0\oplus a=a\;.$$

Does a property of Xor like this exist?

1 Answers1