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Prove or find counterexamples

  1. Dec 1, 2008 #1
    ..using only the definition of the binary product:

    for any sets A, B, C in a universe U:

    (A x B) x C = A x (B x C)

    I have no clue how to even get started with this one. Somebody help me please!!
     
  2. jcsd
  3. Dec 1, 2008 #2
    Typically you would want to show that both inclusions are true....but in this case.....is the element [tex]((a,b),c) = (a,(b,c))[/tex] ?
     
  4. Dec 1, 2008 #3
    Yes, they're equal. It's called the Associative Property of Multiplication.

    The property which states that for all real numbers a, b, and c, their product is always the same, regardless of their grouping:
    (a . b) . c = a . (b . c)
     
  5. Dec 1, 2008 #4
    I'm sorry..I didn't read the your post correctly if that's the case..was thinking cartesian product.
     
  6. Dec 2, 2008 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Then please go back and ask whatever question you are REALLY asking. In your original post, A, B, and C are sets. Now you are telling us that they are real numbers. Also in your first post you asked about proving "A x(B x C)= (A x B)x C" but now you are saying that is the "Associative Property of Multiplication" which apparently you are accepting as true. At this point, I have no idea what your question really is!
     
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