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Thread: Symmetric difference

  1. #1
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    Question Symmetric difference

    Please forgive me in advance if this post is not in the correct section!! Anyways, one of my homework problems is to show that the symmetric difference Δ satisfies the cancellation law, namely, if AΔB=AΔC then B=C. It seems like this is fairly simple however I just can't seem to figure out what to do with this. Thank you for your help!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    A possible way:

    If B\neq C , suppose (without loss of generality) that B\not\subset C

    then

    \exists x: (x\in B\;\wedge\;x\notin C)

    Prove that:

    A \Delta C\not\subset A\Delta B

    or

    A \Delta B\not\subset A\Delta C

    analyzing the cases

    x\in A\;\textrm{or}\;x\notin A.



    Fernando Revilla
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