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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- March 4th 2013, 05:38 PMjojo7777777equivalence 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 - April 11th 2013, 05:46 PMHowDoIMathRe: equivalence relations
When you say R⊆S, does that mean S has more equivalence classes than R (on A)?

- April 12th 2013, 03:48 AMemakarovRe: equivalence relations
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.