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Math Help - Relations help!!

  1. #1
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    Relations help!!

    Hey guys, i'm having some problems answering the last question of my assignment....so hopefully you can help

    8. Test the relation R for the properties of reflexivity, symmetry, antisymmetry and transitivity if R is on the set of positive integers, and is given by (x,y)eR if x<=2y

    *that "e" is supposed to be the, "in the set" character.

    Hope to hear from you soon,
    Thanx in advanc
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  2. #2
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    Hello, Storm20!

    This is a tricky one . . .


    8. Test the relation R for the properties of reflexivity, symmetry, antisymmetry and transitivity
    if R is on the set of positive integers, and is given by: (x,y) \in R\text{ if }x \leq 2y

    Reflexive: . x R x
    . . \text{For all }x\text{, is }x \leq 2x ? . . . No, not reflexive.

    Symmetric: . \text{If }x R\:\!y\text{, then }y R\:\!x.
    . . \text{For all }x,y\text{, does }x \leq 2y \text{ imply }y \leq 2x ? . . . No, not symmtric.

    Antisymmetric: . \text{If }x R\:\!y\text{ and }y\:\!R\:\!x\text{, then: }x = y
    . . \text{Does }x \leq 2y\text{ and }y \leq 2x \text{ imply }x = y ? . . . Yes, it is antisymmetric.

    . . . . (It is true when x = y = 0)

    Transitive: .If  x R\:\! y and y\:\!R\:\! z, then x R z
    . . \text{Does }x \leq 2y\text{ and }y \leq 2z\text{ imply }x \leq 2z ? . . . Yes, it is transitive.

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  3. #3
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    Quote Originally Posted by Storm20 View Post
    Test the relation R for the properties of reflexivity, symmetry, antisymmetry and transitivity if R is on the set of positive integers, and is given by (x,y)eR if x<=2y
    Quote Originally Posted by Soroban View Post
    Reflexive: . x R x
    . . \text{For all }x\text{, is }x \leq 2x ? . . . No, not reflexive.
    Antisymmetric: . \text{If }x R\:\!y\text{ and }y\:\!R\:\!x\text{, then: }x = y
    . . \text{Does }x \leq 2y\text{ and }y \leq 2x \text{ imply }x = y ? . . . Yes, it is antisymmetric.
    . . . . (It is true when x = y = 0)
    Please note that the underlying set is the set of positive integers.
    Any positive integer is less that twice itself. Therefore, the relation is reflexive.


    Now note that: (1,2)\in R \text{ and }  (2,1)\in R \text { but } 1 \not= 2.
    So can the relation be antisymmetric?
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  4. #4
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    Thanx heaps for that guys, the one part of the assignment that I just COULDNT understand. Really appreciate it, thanx for explaining it too.

    peace.
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  5. #5
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    Hello, Plato!

    Quote Originally Posted by Plato View Post

    Please note that the underlying set is the set of positive integers.
    Any positive integer is less that twice itself. Therefore, the relation is reflexive.

    Now note that: (1,2)\in R \text{ and }  (2,1)\in R \text { but } 1 \not= 2.
    So can the relation be antisymmetric?

    Absolutely right on both counts! . . . *blush*
    Somehow, I misunderstood the role of that "2" . . . (slap head)

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