The surjective image of the preimage of a set is equal to the set

up:: 020 MOC Mathematics

With a Surjective Function $f:X\to Y$, we have that

$$\forall y\in Y,\exists x\in X\mid f(x)=y⟺\forall y\in Y,f^{-1}(y)\ne \varnothing$$

This guarantees the reciprocal that The image of the preimage of a set is contained in the set.

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References

• Notas para um Curso de Física-Matemática, João Carlos Alves Barata. Cap. 01>)