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Math Help - What is the equivalence class of (3, 5) with respect to the equivalence relation?

  1. #1
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    What is the equivalence class of (3, 5) with respect to the equivalence relation?

    Q1)
    Code:
    What is the equivalence class of (3, 5) with respect to the equivalence relation in Exercise 16?
    Here is exercise 16:
    Code:
    Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈  R if and only if ad = bc. Show that R is an equivalence relation.
    I've already shown that R is an equivalence relation. Here is my attempt at Q1:

    Code:
    (3, 5)R(a, b) if 5b = 3a, by the definition of R, so [(3, 5)] = {(3a, 5a)|a ∈ Z+}.
    Correct?
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  2. #2
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    Re: What is the equivalence class of (3, 5) with respect to the equivalence relation?

    Surely it is [(3,5)]=\{(a,b)\in\mathbb{Z}^+\times\mathbb{Z}^+:3b=5a\}
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    Re: What is the equivalence class of (3, 5) with respect to the equivalence relation?

    Quote Originally Posted by Plato View Post
    Surely it is [(3,5)]=\{(a,b)\in\mathbb{Z}^+\times\mathbb{Z}^+:3b=5a\}
    Is this an equivalent way to say
    (3, 5)R(a, b) if 5b = 3a, by the definition of R, so [(3, 5)] = {(3a, 5a)|a ∈ Z+}.
    ?
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