- #1

OhyesOhno

- 28

- 0

## Homework Statement

There's this one exam problem that I cannot solve... Here it goes:

Consider the set Z x Z

^{+}. Let R be the relation defined by the following:

for (a,b) and (c,d) in ZxZ

^{+}, (a,b) R (c,d) if and only if ad = bc, where ab is the product of the two numbers a and b.

a) Prove that R is an equivalence relation Z x Z

^{+}

b) Show how R partitions Z x Z

^{+}and describe the equivalence classes

## Homework Equations

For equivalence relations we have to proof that it is reflexive (xRx), symmetric (aRb = bRa) and transitive (aRb bRc hence aRc)

## The Attempt at a Solution

I already did part a... I just have trouble on b... how am I supposed to know the equivalence classes of this?

Last edited: