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Math Help - antisymmetric relations

  1. #1
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    antisymmetric relations

    Let A = {1, 2, 3, . . . , n}, and let R be a relation on A that is antisymmetric.
    (a) What is the maximum number of ordered pairs that can be in R?
    (b) How many antisymmetric relations on A have the size you found in (a)?
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  2. #2
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    Can you write an example of such a maximum relation for n = 3 or n = 4?
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  3. #3
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    antisymmetric relations

    No I have no clue.
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  4. #4
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    Quote Originally Posted by sbankica View Post
    Let A = {1, 2, 3, . . . , n}, and let R be a relation on A that is antisymmetric.
    (a) What is the maximum number of ordered pairs that can be in R?
    (b) How many antisymmetric relations on A have the size you found in (a)?
    Quote Originally Posted by sbankica View Post
    No I have no clue.
    Do you know how to make a table of ordered pairs?
    \begin{array}{lll}<br />
   {(a,a)} & {(a,b)} & {(a,c)}  \\<br />
   {(b,a)} & {(b,b)} & {(b,c)}  \\<br />
   {(c,a)} & {(c,b)} & {(c,c)}  \\ \end{array}

    That is on a set of three elements. There are 9 pairs.
    So there are 2^9 possible relations on a set of three.

    When is a relation not antisymmetric?
    There is a start.

    If you are unable to carry on, then you need to go to instructor for face-to-face help.
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