# Thread: Equivalence relations help

1. ## 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

2. ## Re: Equivalence relations help

Hint: look at the symmetry property.

3. ## Re: Equivalence relations help

more pointedly, clearly (3,1) is in R. is (1,3) in R as well?

4. ## 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.

5. ## Re: Equivalence relations help

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?

6. ## 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