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Verifying an identity

  1. Aug 27, 2011 #1
    I need to verify this identity:

    (A\B)[itex]\Delta[/itex]C = (A[itex]\Delta[/itex]C)[itex]\Delta[/itex](A[itex]\bigcap[/itex]B)

    (with delta standing for the symmetric difference, I don't know the proper latex code)


    I've tried it "brute force" several times, working out each side and simplifying it until the sides are equal (it's likely that I'm messing up a negation somewhere) and I've found this method rather cumbersome. Is there any simpler way to solve this?
     
  2. jcsd
  3. Aug 27, 2011 #2

    I like Serena

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    Hi autre! :smile:

    Have you tried drawing a so called Venn diagram?
     
  4. Aug 27, 2011 #3

    mathman

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    I used Venn diagrams and got the result you are looking for. There are 7 disjoint sets involved. Is that the brute force you tried?
     
  5. Aug 27, 2011 #4
    That's it, mathman. Thanks guys.
     
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