1. ## Equivilence relations, Reflexivity

Hi all,

I am given two relations and asked to prove which one is an equivilence relation for integers.

They are;

$\displaystyle x$~$\displaystyle _{1}y$ if $\displaystyle x^{2}+y^{2}$ is divisible by 5.

$\displaystyle x$~$\displaystyle _{2}y$ if $\displaystyle x^{2}-y^{2}$ is divisible by 4.

The problem i'm having is finding which one has reflexivity.

for example, $\displaystyle 1^{2}+1^{2}=2$ which is not divisble by 5.

and, $\displaystyle k^{2}-k^{2}=0$ for all $\displaystyle k$

So, is zero divisible by 4?

2. ## Re: Equivilence relations, Reflexivity

Think I've got,

zero divided by any integer is zero, but since zero is also an integer then it holds.

Am I right?

3. ## Re: Equivilence relations, Reflexivity

You are right. Zero is divisible by any nonzero integer.

4. ## Re: Equivilence relations, Reflexivity

Originally Posted by Srengam
Think I've got,
zero divided by any nonzero integer is zero, but since zero is also an integer then it holds.
Am I right?
That is correct.