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

    • 3 months ago
  2. satellite73 Group Title
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    \[x^2+1=y^2+1\iff x^2=y^2\iff x=\pm y\]

    • 3 months ago
  3. satellite73 Group Title
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    therefore the equivalence class of \([1]\) is \(\{-1,1\}\)

    • 3 months ago
  4. satellite73 Group Title
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    lot easier than the last one!

    • 3 months ago
  5. kdekle Group Title
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    oh ok! So for [0] the only element is 0?

    • 3 months ago
  6. kdekle Group Title
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    what about [-1/4]?...would it just be {-1/4, 1/4}?

    • 3 months ago
  7. myininaya Group Title
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    looks good

    • 3 months ago
  8. satellite73 Group Title
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    as judge judy would say "the questions get harder"

    • 3 months ago
  9. kdekle Group Title
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    so my answers are correct then?

    • 3 months ago
  10. satellite73 Group Title
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    yes

    • 3 months ago
  11. kdekle Group Title
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    thank you@

    • 3 months ago
  12. satellite73 Group Title
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    yw

    • 3 months ago
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