# Symmetric Difference if/then Proof

1. Jul 30, 2011

### pingi

Hi there,

I'm trying to figure out proving the following:
if X oplus Y = Y oplus X then X = Y

In order to prove it, I need to use the symmetric difference associativity & other characteristics and identities.

Can you please give me a direction?
Please explain the answer as a teacher would, as my skills of proving this kind of arguments are poor.

Thanks! Pingi.

2. Jul 30, 2011

### mathman

What is oplus? Also what kind of things are X and Y (sets, logical variables, other things)?

3. Jul 30, 2011

### pingi

Hi mathman,

Sorry for being unclear about my question and thanks for directing me!

1. X and Y are sets.
2. 'oplus' is an add symbol in circle - ⊕, used to describe the symmetric difference of the two sets (with the XOR operation).

Pingi.

4. Jul 31, 2011

### alexfloo

If it is referring to the symmetric difference or to the exclusive or operations, then I actually don't believe the statement you are trying to prove is true. Both of these operations are commutative, which means that:

X "oplus" Y = Y "oplus" X

regardless of what X and Y are.

If "oplus" means something different, however, then please explain it in more depth.