1. ## equivalence relations

I need help with the following question:

Define a relation R on natural numbers by aRb whenever ab is a square. show R is an equivalence relation.

2. Originally Posted by baker11108
I need help with the following question:

Define a relation R on natural numbers by aRb whenever ab is a square. show R is an equivalence relation.

Where're you stuck? Reflexivity and symmetry are immediate, and transitivity requires a tiny trick: $ac=\frac{(ab)(bc)}{b^2}$ ...

Tonio

3. I am having trouble even before that. We are unsure if we are reading the question right or not. We are not real familiar with equivalence relations. Let's say a=8 and b=2. Then ab=16 which is a square. So aRb by reflexivity because they are elements of natural numbers or what?

4. Originally Posted by baker11108
I am having trouble even before that. We are unsure if we are reading the question right or not. We are not real familiar with equivalence relations. Let's say a=8 and b=2. Then ab=16 which is a square. So aRb by reflexivity because they are elements of natural numbers or what?

You need to re-read your definitions carefully: $8R2$ because $8\cdot 2$ is a square (in the natural numbers, of course)...what has this to do with reflexivity??

Tonio