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Math Help - Relations

  1. #1
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    Relations

    Determine whether each binary relation is reflexive, symmetric, antisemmetric and/or transitive. Justify each one.

    1. The relation R on the natural numbers where aRb means that a has the same number of digits as b.

    2. The relations S on {a,b,c} where

    S = { (a,a), (b,b), (c,c), (a,b), (a,c) , (c,b) }

    3. The relation T on the integers where aTb means....

    | a - b | <= 1.


    Any help please? Thank you
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    Quote Originally Posted by smoothi963 View Post
    Determine whether each binary relation is reflexive, symmetric, antisemmetric and/or transitive. Justify each one.


    1. The relation R on the natural numbers where aRb means that a has the same number of digits as b.
    It is reflexive: aRa
    Ex. (134)R(134)

    It is symmetric: If aRb then bRa
    Ex. (134)R(225) implies (225)R(134)

    It is not antisymmetric because aRb and bRa does not imply a = b
    Ex. (134)R(225) and (225)R(134) but 134 is not equal to 225

    It is transitive: aRb and bRc implies aRc
    Ex. (134)R(225) and (225)R(692) implies (134)R(692)

    -Dan
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by smoothi963 View Post
    Determine whether each binary relation is reflexive, symmetric, antisemmetric and/or transitive. Justify each one.


    2. The relations S on {a,b,c} where

    S = { (a,a), (b,b), (c,c), (a,b), (a,c) , (c,b) }
    It is reflexive:
    aSa, bSb, and cSc

    It is not symmetric:
    aSb but not bSa

    Where S is defined it is antisymmetric:
    aSa and aSa implies aSa
    (sim for b and c)
    But note that bSa, cSa, and bSc do not exist.

    Again, where defined it is transitive.
    There is only 1 allowed example here: aSc and cSb implies aSb.

    -Dan
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    Thank you ...any help on the 3rd question? Thanks alot Top.
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    Quote Originally Posted by smoothi963 View Post
    Determine whether each binary relation is reflexive, symmetric, antisemmetric and/or transitive. Justify each one.
    3. The relation T on the integers where aTb means....
    | a - b | <= 1.
    Recall that 0<1 and |a-b|=|b-a|.
    Consider: 1T2 & 2T3, what about 1T3?
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