Let be a set, the set of all the equivalence relations on and the set of all the functions on . Find .

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- October 19th 2011, 07:36 AMSironEquivalence relation
Let be a set, the set of all the equivalence relations on and the set of all the functions on . Find .

I don't get started ... - October 19th 2011, 07:51 AMemakarovRe: Equivalence relation
Suppose R ∈ E(X) ∩ F(X). Then R is an equivalence relation and a function. Suppose (x, y) ∈ R, i.e., R(x) = y. What can you say about y?

- October 19th 2011, 09:32 AMSironRe: Equivalence relation
If R has to be an equivalence relation and a function at the same time I think y has to be unique.

- October 19th 2011, 10:55 AMPlatoRe: Equivalence relation
- October 19th 2011, 02:56 PMDevenoRe: Equivalence relation
consider a slightly easier question: suppose R is merely reflexive, and also a function. how many reflexive functions are there?