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Cartesian products

  1. Nov 17, 2012 #1
    Hi, everyone. I'm practicing Cartesian products and wanted to see if I was doing this correctly. Here's the problem

    Let A = {x, y, z}, B = {a, b}, C = {1, 3},
    Find B x (C x A) (the x denotes multiplication)

    Now wouldn't B x (C x A) = B x C x A?

    Then we would have:
    B x (C x A) = B x C x A = {(a, 1, x), (a, 1, y), (a, 1, z), (a, 2, x), (a, 2, y), (a, 2, z),
    (b, 1, x), (b, 1, y), (b, 1, z), (b, 2, x), (b, 2, y), (b, 2, z)}

    Is this right?
     
  2. jcsd
  3. Nov 17, 2012 #2

    micromass

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    No, those two aren't equal. We often do identify them, but strictly spoken, they are not equal.
     
  4. Nov 17, 2012 #3
    Yeah, you're right. After a little more looking I found that I was wrong.

    Anyway, here is a second crack at it:

    B x (C x A) =
    {(a, (1, x)), (a, (1, y)), (a, (1, z)), (a, (3, x)), (a, (3, y)), (a, (3, z))
    (b, (1, x)), (b, (1, y)), (b, (1, z)), (b, (3, x)), (b, (3, y)), (b, (3, z))}

    How's this?
     
  5. Nov 17, 2012 #4

    micromass

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    That's right!!
     
  6. Nov 17, 2012 #5
    Thanks!
     
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