# Equivalence relations help

• May 25th 2012, 11:21 PM
mandarep
Equivalence relations help
Hi there,
So I've just been given a revision sheet for my upcoming exams and theres just one question I have no idea how to answer.
So here it is:

Given the following relation R on the set of non-negative integers, test whether R satisfies each of the properties of an equivalence relation.
R = {(x, y) : x ≥ y-1}

Hopefully someone can help me out :)
• May 26th 2012, 12:12 AM
girdav
Re: Equivalence relations help
Hint: look at the symmetry property.
• May 26th 2012, 02:17 AM
Deveno
Re: Equivalence relations help
more pointedly, clearly (3,1) is in R. is (1,3) in R as well?
• May 27th 2012, 12:40 AM
mandarep
Re: Equivalence relations help
Thanks for trying to help guys, but I still don't really understand.
I'm just confused over the whole x ≥ y-1 bit I think, because every example my lecturer went through included a mod.
Thanks anyway though.
• May 27th 2012, 03:33 AM
Siron
Re: Equivalence relations help
Quote:

Originally Posted by mandarep
Thanks for trying to help guys, but I still don't really understand.

What do you not understand? Do you agree the relation is not symmetric thus no equivalence relation?
• May 30th 2012, 12:14 PM
diegzumillo
Re: Equivalence relations help
Maybe it's the notation that's confusing you. R is a set of all pairs of positive integers that obeys the condition x ≥ y-1. The point (3,1) belongs to R, for R to be an equivalence relation (1,3) should also belong to R. Since it doesn't, we have a counter example that proves R is not an equivalence relation. :)

edit: changed "equivalente" to "equivalence". I'm mixing english with portuguese here :P