Thread: Equivilence relations, Reflexivity

Hi all,

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

They are;

~ if is divisible by 5.

~ if is divisible by 4.

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

for example, which is not divisble by 5.

and, for all

So, is zero divisible by 4?

Think I've got,

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

Am I right?

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

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.