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?

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

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

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

Quote:

Originally Posted by

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

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+}.

?