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Math Help - Show a property for all elements

  1. #1
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    Show a property for all elements

    I have a definition of a property and I need to show that a structure has that property?
    How can I do it? I know indeed that the structure has that property. I tried that property for some elements and It worked now I want to show that works for all.
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  2. #2
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    Re: Show a property for all elements

    Quote Originally Posted by jake28 View Post
    I have a definition of a property and I need to show that a structure has that property?
    How can I do it? I know indeed that the structure has that property. I tried that property for some elements and It worked now I want to show that works for all.
    That is entirely too vague to have us even to attempt to address. Please post an exact statement of the problem along with what work you have done on it.
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  3. #3
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    Re: Show a property for all elements

    Quote Originally Posted by Plato View Post
    That is entirely too vague to have us even to attempt to address. Please post an exact statement of the problem along with what work you have done on it.
    Basically I have the definition of the latin square property and I need to show that a given structure has that property.
    Property: For all elements a,b belonging to G , there exists a unique x,y belonging to G, such that a*x=b and y*a=b

    G=
    1 2 3 4
    2 1 4 3
    3 4 1 2
    4 3 2 1
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  4. #4
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    Re: Show a property for all elements

    that property means that each b in G occurs exactly once in each row, and each column of your table.

    there is a unique x in G such that a*x = b means that in the row corresponding to "a", b only occurs in the "x" column.

    there is a unique y in G such that y*a = b means that in the column corresponding to "a", b only occurs the "y" row.

    for the table you have given, you may verify this by counting instances of each element of {1,2,3,4} in every row, and column.
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  5. #5
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    Re: Show a property for all elements

    So that means that if I show that each element only occurs once in every row of G, I prove that the G has the latin square property, right?
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