## kdekle Group Title 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] 3 months ago 3 months ago

1. kdekle Group Title

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. satellite73 Group Title

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

3. satellite73 Group Title

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

4. satellite73 Group Title

lot easier than the last one!

5. kdekle Group Title

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

6. kdekle Group Title

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

7. myininaya Group Title

looks good

8. satellite73 Group Title

as judge judy would say "the questions get harder"

9. kdekle Group Title

so my answers are correct then?

10. satellite73 Group Title

yes

11. kdekle Group Title

thank you@

12. satellite73 Group Title

yw