There is a class with more than one element if, and only if there are such that , and that means is not one-to-one.
Since for any propositions , , we've finished.
(just two contrapositions)
Let A be a set. For every set B and total function f:A->B we define a relation R on A by R={(x,y) belonging to A*A:f(x)=f(y)}
*belonging to - because i dont know how to make the symbole....
Prove that f is one-to-one if and only if the equivalence classes of R are all singletones