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Math Help - Set Theory Question

  1. #1
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    Set Theory Question

    1) Which of the following sets are equal?
    a) {1, 2, 3}
    b) {3, 2, 1, 3}
    c) {3, 1, 2, 3}
    d) {1, 2, 2, 3}


    Is this as simple as saying b and c are equal because they contain the same numbers? Or is it more complicated than that?
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  2. #2
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    Re: Set Theory Question

    Yes that is correct.
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  3. #3
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    Re: Set Theory Question

    Is there anyway to show work for this problem? Or is just saying "b and c are equal because they contain the same set of numbers" enough?
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  4. #4
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    Re: Set Theory Question

    Hmm, my friend just told me that they are equal if every element of one is a subset of the other and that they are all equal.

    Now I'm more confused lol.
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  5. #5
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    Re: Set Theory Question

    Two sets are equal if they contain exactly the same elements and nothing else. It's as simple as that...
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  6. #6
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    Re: Set Theory Question

    Quote Originally Posted by rhymin View Post
    1) Which of the following sets are equal?
    a) {1, 2, 3}
    b) {3, 2, 1, 3}
    c) {3, 1, 2, 3}
    d) {1, 2, 2, 3}

    There is only one set in the list above: : \{1,2,3\}

    \{1, 2, 3\}=\{3, 2, 1, 3\}=\{3, 1, 2, 3\}=\{1, 2, 2, 3\}
    Last edited by Plato; March 25th 2013 at 04:54 PM.
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  7. #7
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    Re: Set Theory Question

    Plato's point is that a set does not have the same object multiple times. However, some texts would simply ignore the multiple occurances and say that all those sets are the same- and would be better written as just {1, 2, 3}.
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  8. #8
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    Re: Set Theory Question

    Hmm, I'm confused again...sorry for my ignorance.
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  9. #9
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    Re: Set Theory Question

    Oh, so they are all the same really? Since duplicates don't matter?
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  10. #10
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    Re: Set Theory Question

    Quote Originally Posted by rhymin View Post
    Oh, so they are all the same really? Since duplicates don't matter?

    Both of these sets \{1\}~\&~\{1,1\} has only one element.
    Sets are determined only by its contents.
    Can you think of these in those terms?
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  11. #11
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    Re: Set Theory Question

    Yes, thank you!
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  12. #12
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    Re: Set Theory Question

    All 4 are different ways of writing the same set. The most natural way to write this set is {1,2,3}.
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