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Symmetric Difference if/then Proof

  1. Jul 30, 2011 #1
    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. jcsd
  3. Jul 30, 2011 #2


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    What is oplus? Also what kind of things are X and Y (sets, logical variables, other things)?
  4. Jul 30, 2011 #3
    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).

  5. Jul 31, 2011 #4
    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.
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