Thread: Help with Relations equivalence Q

1. Help with Relations equivalence Q

Hi I would be grateful for replies on how to do this Q.

Define a relation R on R^2 (reals squared) by

(x1,y1)R(x2,y2) iff (x1)^2 + (y1)^2 = (x2)^2 + (y2)^2

Prove that R is an equivalence relation. Describe geometrically the equivalence classes.

Thanks

2. Re: Help with Relations equivalence Q

Originally Posted by James7361539
Hi I would be grateful for replies on how to do this Q.

Define a relation R on R^2 (reals squared) by

(x1,y1)R(x2,y2) iff (x1)^2 + (y1)^2 = (x2)^2 + (y2)^2

Prove that R is an equivalence relation. Describe geometrically the equivalence classes.

Thanks
you need to show

reflexivity, i.e. aRa

symmetry, i.e. aRb <--> bRa

transitivity, i.e. (aRb,bRc) --> aRc

I don't see that restricting your points to Q makes any difference.

given that your relation is just the square of the distance between the points (x1,y1) and (x2,y2) the geometric interpretation of the equivalence classes should be pretty clear.

3. Re: Help with Relations equivalence Q

Originally Posted by romsek
I don't see that restricting your points to Q makes any difference.
I think that the OP is using Q for the word "question" and not $\mathbb{Q}$.

4. Re: Help with Relations equivalence Q

Originally Posted by Plato
I think that the OP is using Q for the word "question" and not $\mathbb{Q}$.
yes quite. That will teach me to start this before finishing my coffee.