## anonymous 2 years ago Let R be the relation xRy if and only if x^2+1=y^2+1. Since it is an equivalence relation, list all the elements of the equivalence classes [1], [0], [-1/4]

1. anonymous

I have already proven it's an equivalence relation but we didn't go over classes so much so I'm a bit confused

2. anonymous

$x^2+1=y^2+1\iff x^2=y^2\iff x=\pm y$

3. anonymous

therefore the equivalence class of $$[1]$$ is $$\{-1,1\}$$

4. anonymous

lot easier than the last one!

5. anonymous

oh ok! So for [0] the only element is 0?

6. anonymous

what about [-1/4]?...would it just be {-1/4, 1/4}?

7. myininaya

looks good

8. anonymous

as judge judy would say "the questions get harder"

9. anonymous

so my answers are correct then?

10. anonymous

yes

11. anonymous

thank you@

12. anonymous

yw