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How can we check that this operation is associative ?

  1. Nov 2, 2012 #1
    hello , there is an example here say that the binary operation which we denote it Δ is associative .
    Δ is defiened as follows :
    if A,B are two sets then
    AΔB=(A-B)U(B-A). and Δ is associative . but the proof is omitted . and I need to know the proof .
  2. jcsd
  3. Nov 2, 2012 #2


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    So, what did you attempt? Where are you stuck?
  4. Nov 2, 2012 #3


    Staff: Mentor

    start by subbing in the the union definition and then rearrange terms.

    (A ^ B) ^ C ) = ( ( A - B ) U ( B - A ) - C ) U ( C - ( A - B ) U ( B - A ) )

    now show some work.
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