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kdekle

  • 7 months 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]

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  1. kdekle
    • 7 months ago
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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

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

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

  4. satellite73
    • 7 months ago
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    lot easier than the last one!

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

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

  7. myininaya
    • 7 months ago
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    looks good

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

  9. kdekle
    • 7 months ago
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    so my answers are correct then?

  10. satellite73
    • 7 months ago
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    yes

  11. kdekle
    • 7 months ago
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    thank you@

  12. satellite73
    • 7 months ago
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    yw

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