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Math Help - Relations and properties

  1. #1
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    Post Relations and properties

    Suppose that R and S are reflexive relations on a set A. Prove or disprove this statements:
    a.  R \cup S is reflexive
    b.  R \cap S is reflexive
    c.  R-S is irreflexive

    for part a and b I answered that it is true and part c is false. is this right?
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  2. #2
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    Quote Originally Posted by TheRekz View Post
    Suppose that R and S are reflexive relations on a set A. Prove or disprove this statements:
    a.  R \cup S is reflexive
    b.  R \cap S is reflexive
    c.  R-S is irreflexive

    for part a and b I answered that it is true and part c is false. is this right?
    Hi TheRekz .

    I agree with you that : a,b are true and c is false .
    Last edited by le_su14; July 10th 2007 at 08:20 PM.
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  3. #3
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    why is  R \cup S irreflexive??
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  4. #4
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    Quote Originally Posted by TheRekz View Post
    why is  R \cup S irreflexive??
    I'm sorry , I made a mistake .
    You are true .

    a/  \forall x \in R \cup S , x \in S or  y \in R . So xRx .  R \cup S is reflexive .
    b/  \forall x \in R \cap S , x \in S and  y \in R . So xRx . R \cap S is reflexive .
    c/  \forall x \in R - S , x \in R reflexive. So xRx . R - S is reflexive .
    Last edited by le_su14; July 10th 2007 at 08:32 PM.
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  5. #5
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    The set \Delta _A  = \left\{ {(x,x)|x \in A} \right\} is known as the diagonal relation on set A. Any relation, R, on A is reflexive if and only if  \Delta _A  \subseteq R . Using that characterization, it is easy to see the three statements are true.
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  6. #6
    ali.irfan.kurt
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    Quote Originally Posted by le_su14 View Post
    I'm sorry , I made a mistake .
    You are true .

    a/  \forall x \in R \cup S , x \in S or  y \in R . So xRx .  R \cup S is reflexive .
    b/  \forall x \in R \cap S , x \in S and  y \in R . So xRx . R \cap S is reflexive .
    c/  \forall x \in R - S , x \in R reflexive. So xRx . R - S is reflexive .

    Hi guys,

    I'm confused. Are above statements correct? Is R S reflexive? If so how did you come up with the result.

    Thanks,
    James
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  7. #7
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    Quote Originally Posted by ali.irfan.kurt View Post
    Are above statements correct? Is R S reflexive?
    The relation R-S is irreflexive! Because S is reflexive, the diagonal has been removed.
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