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Let f:a to b be a surjective map of sets prove that the relation a if and only if f(a) = f(b) is an equivalence relation whose equivalence classes are the fibers of f

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Answer:

Step-by-step explanation:

Denote this equivalence relation by [tex]"\sim"[/tex] (i.e, [tex]a\sim b[/tex] if and only if [tex]f(a)=f(b)[/tex]), is clear that [tex]a\sim a[/tex] is an equivalence relation since [tex]"="[/tex] is. Now, by definition we have that [tex][a]=\{b\sim a \mid f(a)=f(b) \}=f^{-1}(a)[/tex].

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