Question

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

Answer 1

Explanation:

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