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Math Help - define a relation...

  1. #1
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    define a relation...

    i have a question and i am stuck on the first part was wondering if you could help.

    Let R be the set of real numbers. Define a relation R(subscript1) on the set R as follows: m R(subscript1) n whenever n-m congruent to 0(mod24).

    First off how do i define this relation?
    I then have to proove R(subscript1) is an equivalence relation but i want to give this a bash first once i managed to define the relation.
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  2. #2
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    Quote Originally Posted by ad53ggz View Post
    Let R be the set of real numbers. Define a relation R(subscript1) on the set R as follows: m R(subscript1) n whenever n-m congruent to 0(mod24). First off how do i define this relation?

    Is R a collection of ordered pairs? If so it is a relation on \Re.

    Quote Originally Posted by ad53ggz View Post
    Let R be the set of real numbers. Define a relation R(subscript1) on the set R as follows: m R(subscript1) n whenever n-m congruent to 0(mod24). Is it an equivalence relation.

    You must show that R is reflexive, symmetric & transitive.
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  3. #3
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    Quote Originally Posted by Plato View Post
    Is R a collection of ordered pairs? If so it is a relation on \Re.

    sorry but dont get this bit

    You must show that R is reflexive, symmetric & transitive.

    yeah get this bit
    I just dont get that first bit Is R a collection of ordered pairs? If so it is a relation on \Re.
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    Quote Originally Posted by ad53ggz View Post
    I just dont get that first bit Is R a collection of ordered pairs? If so it is a relation on \Re.
    ordered pairs is what you would know as coordinates, sort of

    like (m,n) is an ordered pair.

    now, a relation is a set of such pairs. thus, saying mR_1n is the same as saying (m,n) \in R_1, that is, the ordered pair (m,n) is an element of the (set) relation R_1. note that the relation is on the real numbers, this means that m and n are real numbers

    the relation has been defined for you, you do not have to do that. simply prove it is an equivalence relation in the way Plato said. you do know the definitions of "reflexive", "symmetric" and "transitive", right?
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  5. #5
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    Quote Originally Posted by ad53ggz View Post
    I just dont get that first bit Is R a collection of ordered pairs? If so it is a relation on \Re.
    Do you know the definition of relation?
    A relation on \Re is a subset of \Re \times \Re.
    Does you R define a relation?
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  6. #6
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    yeah pretty sure,

    reflexive if for all x in R xRx
    Symettric if for all x and y in R , xRy implies yRx
    Transitive of for x,y&z in R, xRy and yRz implies xRZ.

    i will have a look to see how apply it to this question
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  7. #7
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    Quote Originally Posted by Plato View Post
    Do you know the definition of relation?
    A relation on \Re is a subset of \Re \times \Re.
    Does you R define a relation?
    SO i dont actually need to define anything just go on to show its equivalant
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ad53ggz View Post
    yeah pretty sure,

    reflexive if for all x in R xRx
    Symettric if for all x and y in R , xRy implies yRx
    Transitive of for x,y&z in R, xRy and yRz implies xRZ.

    i will have a look to see how apply it to this question
    yes, good.

    now, remember how to interpret congruences

    saying m - n \equiv 0 \mod{24}

    is the same as saying 24 \mid (m - n)

    which is the same as saying m - n = 24k for some integer k

    use any or all of these forms as they are convenient for you
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  9. #9
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ad53ggz View Post
    SO i dont actually need to define anything just go on to show its equivalant
    correct, they gave you the definition. they told you to define it "as follows.." meaning, they are saying, "this is how we want you to define it"

    the definition is done, just state it and continue with the proof
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  10. #10
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    cheers think i have got it now.
    Last edited by ad53ggz; December 2nd 2008 at 10:29 AM.
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  11. #11
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    Hello, ad53ggz!

    Let R be the set of real numbers.

    Define a relation R_1 on set R as follows: . m\:R_1\:n\text{ whenever }n-m \equiv 0\text{ (mod 24)}

    First off, how do i define this relation?

     n-m \equiv 0 \text{ (mod 24)} .means . n-m\text{ is a multiple of 24.}

    That is: . n - m \:=\:24a\text{ for some integer }a.




    I then have to prove R_1 is an equivalence relation.

    You should be able to handle this part now . . .

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  12. #12
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    thanks everybody problem solved
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  13. #13
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    .
    Last edited by ad53ggz; December 3rd 2008 at 12:13 PM.
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