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Math Help - discrete math - equivalence relation

  1. #1
    Junior Member
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    discrete math - equivalence relation

    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
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  2. #2
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    There is a class with more than one element if, and only if there are x,y \in A,\ x\neq y such that f(x)=f(y), and that means f is not one-to-one.

    Since for any propositions P,Q, (P\Leftrightarrow Q )\Leftrightarrow (\lnot P\Leftrightarrow \lnot Q), we've finished.

    (just two contrapositions)
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