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

• Nov 18th 2013, 09:30 AM
lamentofking
What is the equivalence class of (3, 5) with respect to the equivalence relation?
Q1)
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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?
• Nov 18th 2013, 09:47 AM
Plato
Re: What is the equivalence class of (3, 5) with respect to the equivalence relation?
Surely it is $[(3,5)]=\{(a,b)\in\mathbb{Z}^+\times\mathbb{Z}^+:3b=5a\}$
• Nov 18th 2013, 10:09 AM
lamentofking
Re: What is the equivalence class of (3, 5) with respect to the equivalence relation?
Quote:

Originally Posted by Plato
Surely it is $[(3,5)]=\{(a,b)\in\mathbb{Z}^+\times\mathbb{Z}^+:3b=5a\}$

Is this an equivalent way to say
Quote:

(3, 5)R(a, b) if 5b = 3a, by the definition of R, so [(3, 5)] = {(3a, 5a)|a ∈ Z+}.
?