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Math Help - equivalence relations

  1. #1
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    equivalence relations

    Suppose R is an equivalence relation on a set A, with four equivalence classes.
    How many different equivalence relations S on A are there for which R⊆S?
    Thanking you in anticipation
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  2. #2
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    Re: equivalence relations

    When you say R⊆S, does that mean S has more equivalence classes than R (on A)?
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  3. #3
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    Re: equivalence relations

    Quote Originally Posted by HowDoIMath View Post
    When you say R⊆S, does that mean S has more equivalence classes than R (on A)?
    No, I assume R ⊆ S means that R is a subset of S where both R and S are viewed as subsets of A x A. That is, S is coarser than R and thus has fewer equivalence classes than R.

    The number of such S equals the number of equivalence relations on 4 elements. It is probably easier to calculate this number manually than to apply a general formula.
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