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Math Help - Properties of Relations

  1. #1
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    Properties of Relations

    course: Foundations of Higher Math

    Let A=\left\{1,2,3,4\right\}. Give an example of a relation on A that is reflexive and transitive, but not symmetric.

    My question is, does my relation have to include all of the pairs \left\{(1,1),(2,2),(3,3),(4,4)\right\} to be reflexive?

    For example, say my relation is R=\left\{(1,1),(3,3),(1,3)\right\}.
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  2. #2
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    Re: Properties of Relations

    Quote Originally Posted by MadSoulz View Post
    course: Foundations of Higher Math

    Let A=\left\{1,2,3,4\right\}. Give an example of a relation on A that is reflexive and transitive, but not symmetric.

    My question is, does my relation have to include all of the pairs \Delta_A=\left\{(1,1),(2,2),(3,3),(4,4)\right\} to be reflexive?

    For example, say my relation is R=\left\{(1,1),(3,3),(1,3)\right\}.
    Any reflexive relation on A must contain \Delta_A as a subset.
    Thanks from MadSoulz
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    Re: Properties of Relations

    Quote Originally Posted by Plato View Post
    Any reflexive relation on A must contain \Delta_A as a subset.
    Perhaps my professor made a mistake in class.

    We had S=\left\{1,2,3\right\} and said that
    R= \left\{(1,1),(2,2)\right\} was a reflexive relation.
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    Re: Properties of Relations

    Quote Originally Posted by MadSoulz View Post
    Perhaps my professor made a mistake in class.

    We had S=\left\{1,2,3\right\} and said that
    R= \left\{(1,1),(2,2)\right\} was a reflexive relation.
    Are you sure you heard correctly? R is a reflexive relation on {1, 2} but not on {1, 2, 3}.
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    Re: Properties of Relations

    Quote Originally Posted by HallsofIvy View Post
    Are you sure you heard correctly? R is a reflexive relation on {1, 2} but not on {1, 2, 3}.
    Yes, he wrote the following table on the board then filled it in himself.

    R_3 was the only one that had an 'X' for reflexive.
    Attached Thumbnails Attached Thumbnails Properties of Relations-screen-shot-2013-11-16-2.54.44-pm.png  
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    Re: Properties of Relations

    Quote Originally Posted by HallsofIvy View Post
    Are you sure you heard correctly? R is a reflexive relation on {1, 2} but not on {1, 2, 3}.
    Here's the entire Powerpoint slide
    Attached Thumbnails Attached Thumbnails Properties of Relations-screen-shot-2013-11-16-3.09.53-pm.png  
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    Re: Properties of Relations

    Quote Originally Posted by MadSoulz View Post
    R_3 was the only one that had an 'X' for reflexive.
    R_3 is not even close to being reflexive: it does not contain a single pair from the diagonal.
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    Re: Properties of Relations

    Quote Originally Posted by emakarov View Post
    R_3 is not even close to being reflexive: it does not contain a single pair from the diagonal.
    Sorry

    EDIT: R_3 was the only one that had an 'X' for *not* reflexive.
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    Re: Properties of Relations

    R_3 was the only relation that was not reflexive. Forgive my earlier failed explanation
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    Re: Properties of Relations

    Quote Originally Posted by MadSoulz View Post
    R_3 was the only one that had an 'X' for *not* reflexive.
    Actually I suspected that was the case

    R_3 is the only one in the list that is irreflexive: i.e. \Delta_S\cap R_3=\emptyset~.

    I wonder if that is what your instructor meant?
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    Re: Properties of Relations

    Quote Originally Posted by Plato View Post
    Actually I suspected that was the case

    R_3 is the only one in the list that is irreflexive: i.e. \Delta_S\cap R_3=\emptyset~.

    I wonder if that is what your instructor meant?
    Perhaps. I'll have to ask him on Monday. He doesn't answer emails on weekends.
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    Re: Properties of Relations

    Thanks to you all for your time.
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