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Math Help - Relation ( Equivalence Relation)

  1. #1
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    Relation ( Equivalence Relation)

    Which of these relation on the set of all people are equivalence relation ? Determine the properties of an equivalence relation that the other lack.

    (1) {(a,b) | a and b are the same age}
    (2) {(a,b) | a and b have the same parents}
    (3) {(a,b) | a and b share a common parents}
    (4) {(a,b) | a and b have met}
    (5) {(a,b) | a and b speak common language}

    Appreciate your reply.
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  2. #2
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    Why don’t you show us some of your own work on these?
    Here is a hint. Often such words as “equal or the same as” point to an equivalence relation.
    But be careful, for #2 & #3 look a lot alike, however one is an equivalence relation and the other is not.
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  3. #3
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    I do not even know how to begin or solve this otherwise i would have showed you some of my work.
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  4. #4
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    As far as i understand (1) and (2) are Equivalence Relation but i am not sure about the other ones that are they reflexivity,symmetry and transitive.

    would you please help me with this ??
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  5. #5
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    Go and have a sit-down with your lecturer/teacher/instructor.
    Tell that person just how much you do not understand.
    Having done that and if you still do not understand any of this then drop the course.
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  6. #6
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    Quote Originally Posted by bhuvan View Post
    Which of these relation on the set of all people are equivalence relation ? Determine the properties of an equivalence relation that the other lack.

    (1) {(a,b) | a and b are the same age}
    (2) {(a,b) | a and b have the same parents}
    (3) {(a,b) | a and b share a common parents}
    (4) {(a,b) | a and b have met}
    (5) {(a,b) | a and b speak common language}

    Appreciate your reply.

    (4) is not reflexive so not eqivalence
    (5)5 is also equivalent relation
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  7. #7
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    I meet myself every morning in my mirror (I guess the answer depends on what means to meet ); what is sure is that (4) isn't transitive. (If a friend of you knows somebody, that doesn't mean you also know him/her)

    (5) is reflexive, symmetric, but... if I speak french, my friend speaks french and spanish, and another guy speaks only spanish, transitivity is dead.


    Of course the problem when you want to apply mathematical definitions to "real" cases is that real cases must be very well defined to avoid ambiguity (i.e. I may have done wrong)
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  8. #8
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    reply on ambiguity

    ya your interpretation is pity correct but if u speak purely mathematically then b and c must speak comman language and thats enough for me to show that they are transitive however in real life even the set of lamguages will come into play means exactly how many languages are comman between them and how many languages one can speak considering they are all of same language reason its transitive.
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  9. #9
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    I don't really have doubts for 5).
    Look at this similar example, but purely mathematic: \forall a,b\in \mathbb{N},\ aRb \Leftrightarrow a,b have a common prime divisor.

    3R6 , 6R2 , but pgcd(2,3)=1, so we don't have 2R3.
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