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Math Help - Abstract Algebra Reflexive Properties

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    Abstract Algebra Reflexive Properties

    Need help understanding reflexive properties of Abstract algebra. If A = {1, 2, 3} what are its reflexive properties?
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    Quote Originally Posted by henshilwood View Post
    Need help understanding reflexive properties of Abstract algebra. If A = {1, 2, 3} what are its reflexive properties?
    Given a set A and a relation R on A a reflexsive property is defined as if yRx then, xRy. Now the meaning of yRx is (y,x)\in R.

    The reflexive property appears in two specific types of relations. An equivalence relation used a lot in abstract algebra and partial ordering relation a favorite in set theory.

    I cannot answer thy question for thee has not defined a relation of \{1,2,3\}
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    Quote Originally Posted by ThePerfectHacker View Post
    Given a set A and a relation R on A a reflexsive property is defined as if yRx then, xRy. Now the meaning of yRx is (y,x)\in R.

    The reflexive property appears in two specific types of relations. An equivalence relation used a lot in abstract algebra and partial ordering relation a favorite in set theory.

    I cannot answer thy question for thee has not defined a relation of \{1,2,3\}
    The specific question out of the book is "Let A be the set {1, 2, 3}. List the ordered pairs in a relation on A which is reflexive."
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    Quote Originally Posted by henshilwood View Post
    The specific question out of the book is "Let A be the set {1, 2, 3}. List the ordered pairs in a relation on A which is reflexive."
    Sorry, but the important thing is that you understand what I said. Relations are fundamental to understand algebra.

    Okay the following set,
    \{ (1,2),(2,1),(1,3),(3,1),(2,3), (3,2)\}
    Is a relation on \{1,2,3\}.
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    Quote Originally Posted by ThePerfectHacker View Post
    Sorry, but the important thing is that you understand what I said. Relations are fundamental to understand algebra.

    Okay the following set,
    \{ (1,2),(2,1),(1,3),(3,1),(2,3), (3,2)\}
    Is a relation on \{1,2,3\}.
    We should note that the relation that TPH provided is, in a sense, "maximal" since it includes all the points in A. But we could also say that: \{ (1,2), (2,1) \} is also a reflexive relation on A. (And similar other relations.)

    -Dan
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    Quote Originally Posted by topsquark View Post
    We should note that the relation that TPH provided is, in a sense, "maximal" since it includes all the points in A. But we could also say that: \{ (1,2), (2,1) \} is also a reflexive relation on A. (And similar other relations.)

    -Dan
    Funny thing is I was working with the symmettic relation all of time and did not realize it. Hope I did not confuse the reader.
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    The relation \Delta _A  = \left\{ {\left( {1,1} \right),\left( {2,2} \right),\left( {3,3} \right)} \right\} is called the diagonal relation. Any relation that contains the diagonal is a reflexive relation. Now there are 6 off-diagonal pairs in AxA. Thus, there are 2^6 subsets of the off-diagonal pairs. Unite each of those with the diagonal to get a reflexive relation on A. That is, there are 2^6 reflexive relations on A.
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    Quote Originally Posted by Plato View Post
    The relation \Delta _A  = \left\{ {\left( {1,1} \right),\left( {2,2} \right),\left( {3,3} \right)} \right\} is called the diagonal relation. Any relation that contains the diagonal is a reflexive relation. Now there are 6 off-diagonal pairs in AxA. Thus, there are 2^6 subsets of the off-diagonal pairs. Unite each of those with the diagonal to get a reflexive relation on A. That is, there are 2^6 reflexive relations on A.
    But the problem is the user was asking for a relation that is reflexsive but not symettric and transitive. The reason why I know is because I spoke with him on PM.
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    Well, that is certainly not what he wrote.
    I took him at his word: “Need help understanding reflexive properties ..”.
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