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 ...
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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?
If R has to be an equivalence relation and a function at the same time I think y has to be unique.
Originally Posted by Siron If R has to be an equivalence relation and a function at the same time I think y has to be unique. Suppose that Is it true that . Suppose that and is it possible that
consider a slightly easier question: suppose R is merely reflexive, and also a function. how many reflexive functions are there?
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