# Help with Relations equivalence Q

• Mar 17th 2014, 08:37 AM
James7361539
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
• Mar 17th 2014, 08:43 AM
romsek
Re: Help with Relations equivalence Q
Quote:

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.
• Mar 17th 2014, 09:02 AM
Plato
Re: Help with Relations equivalence Q
Quote:

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}\$.
• Mar 17th 2014, 09:12 AM
romsek
Re: Help with Relations equivalence Q
Quote:

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.