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Math Help - Partial orders

  1. #1
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    Partial orders

    Hi,

    I have to prove that R \cap (BxB) is a partial order on B, supposed that R is a partial order on A and B \subseteq A.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by TheFangel View Post
    Hi,

    I have to prove that R \cap (BxB) is a partial order on B, supposed that R is a partial order on A and B \subseteq A.
    You have three things to prove, and writing (a, b) \in R for a \leq b or a R b or whatever,

    (a, a) \in R

    (a, b) \in R \text{ and }(b, a) \in R \Rightarrow a=b

    (a, b) \in R \text{ and } (b, c) \in R \Rightarrow (a, c) \in R.

    You know this holds for all a, b, c \in A and you need to show that it holds for all a, b, c \in B \subseteq A. However, as a, b, c \in B \Rightarrow a, b, c \in A then...
    Last edited by Swlabr; May 6th 2010 at 01:41 AM.
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