# Logic proof

1. Feb 21, 2005

### gnome

Given that XOR is defined by $((X \wedge \neg Y) \vee (\neg X \wedge Y))$, in order to prove that XOR is commutative is it sufficient to prove that
$((X \wedge \neg Y) \vee (\neg X \wedge Y)) \supset ((Y \wedge \neg X) \vee (\neg Y \wedge X))$
is a tautology?

2. Feb 21, 2005

### Hurkyl

Staff Emeritus

If (X xor Y), then (Y xor X).

Is that the same as X xor Y = Y xor X?

(no)

Now, in general you would leave the last step implicit, because it's fairly routine, but I imagine you're interested in full rigor.

3. Feb 21, 2005

### gnome

OK, I'd like to retract that ridiculous statement before I get banned. :rofl: :rofl: :rofl:

Maybe I'd better get some sleep... :zzz: