Question

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]

Answer 1

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

Answer 2

\[x^2+1=y^2+1\iff x^2=y^2\iff x=\pm y\]

Answer 3

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

Answer 4

lot easier than the last one!

Answer 5

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

Answer 6

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

Answer 7

looks good

Answer 8

as judge judy would say
"the questions get harder"

Answer 9

so my answers are correct then?

Answer 10

yes

Answer 11

thank you@

Answer 12

yw