anonymous
  • anonymous
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]
Mathematics
schrodinger
  • schrodinger
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anonymous
  • 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
anonymous
  • anonymous
\[x^2+1=y^2+1\iff x^2=y^2\iff x=\pm y\]
anonymous
  • anonymous
therefore the equivalence class of \([1]\) is \(\{-1,1\}\)

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anonymous
  • anonymous
lot easier than the last one!
anonymous
  • anonymous
oh ok! So for [0] the only element is 0?
anonymous
  • anonymous
what about [-1/4]?...would it just be {-1/4, 1/4}?
myininaya
  • myininaya
looks good
anonymous
  • anonymous
as judge judy would say "the questions get harder"
anonymous
  • anonymous
so my answers are correct then?
anonymous
  • anonymous
yes
anonymous
  • anonymous
thank you@
anonymous
  • anonymous
yw

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