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Math Help - Partiel order

  1. #1
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    Partiel order

    Is there a smart way to dertermine wether a relation is called a partiel order.

    For a relation to be a partiel order (dont know how you describe it) it has to be reflexive, antisymmetric and transitive.

    reflexive: aRb <=> aRa
    tansitive aRb <=> aRb and bRc => aRc
    antisymmetric: aRb <=> aRb and bRa => a=b

    Can you help me out to dertermine these?

    xR1y <=>x + y = or <0

    xR2y <=>x y = or <0

    xR3y <=>x + y < 0
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  2. #2
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    Quote Originally Posted by Madspeter View Post
    Is there a smart way to dertermine wether a relation is called a partial order.

    For a relation to be a partial order (dont know how you describe it) it has to be reflexive, antisymmetric and transitive.

    reflexive: aRb <=> aRa
    tansitive aRb <=> aRb and bRc => aRc
    antisymmetric: aRb <=> aRb and bRa => a=b

    Can you help me out to dertermine these?

    xR1y <=>x + y = or <0

    xR2y <=>x y = or <0

    xR3y <=>x + y < 0
    (-2,-1)\in R_1~\&~(-1,-2)\in R_1\text{ but is it true that }-2\ne -1?

    (-2,-1)\in R_2\text{ but is it true that }(-1,-2)\in R_2 ?

    \text{Is it true that }(0,0)\in R_3 ?
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  3. #3
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    Quote Originally Posted by Plato View Post
    (-2,-1)\in R_1~\&~(-1,-2)\in R_1\text{ but is it true that }-2\ne -1?

    here you see if the if the relation is antisymmetric? which is true if it had been "x not related to y."


    (-2,-1)\in R_2\text{ but is it true that }(-1,-2)\in R_2 ?

    I can't see what you are doing here.

    \text{Is it true that }(0,0)\in R_3 ?

    here you see if its reflexive which is isnt.


    can you elaborate on how you decide wether its partiel or not.
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  4. #4
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    Quote Originally Posted by Madspeter View Post
    here you see if its reflexive which is isnt.
    can you elaborate on how you decide wether its partiel or not.
    First the English spelling is partial.

    I showed that R_2 is not symmetric.

    Also showed that R_1 is not antisymmetric.
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  5. #5
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    Quote Originally Posted by Plato View Post
    First the English spelling is partial.

    I showed that R_2 is not symmetric.

    Also showed that R_1 is not antisymmetric.


    But for a relation to be partial it is not needed to be symmetric, or?
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  6. #6
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    Quote Originally Posted by Madspeter View Post
    But for a relation to be partial it is not needed to be symmetric, or?
    You are correct about that. I wanted to show how things work.
    Is R_2 transitive?
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  7. #7
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    Quote Originally Posted by Plato View Post
    You are correct about that. I wanted to show how things work.
    Is R_2 transitive?

    I can't really figure that out, Im afraid.

    Maybe something with -1 - (-2) < or = 0 => -2 - z < or = 0

    then -1 - z < or = 0.

    Im quite lost acutally.
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  8. #8
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    Do you understand this whole area?
    \left\{ \begin{gathered}<br />
  x - y \leqslant 0 \hfill \\<br />
  y - z \leqslant 0 \hfill \\ <br />
\end{gathered}  \right.\, \Rightarrow \,x - z \leqslant 0
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  9. #9
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    Isnt that basically what i wrote about transitivity?

    xRy and yRz => xRz

    However, I have difficulty seeing how yRz can be proven.
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  10. #10
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    Quote Originally Posted by Madspeter View Post
    Isnt that basically what i wrote about transitivity?
    xRy and yRz => xRz
    However, I have difficulty seeing how yRz can be proven.
    You are in need of some 'sit down' help.
    Please go to your instructor/tutor for more help.
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  11. #11
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    Im afraid I can't afford that.

    Thanks for your help anyway.
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