Mapping/Surjective and preimage injective/Exercise

Let ${}L$ and ${}M$ denote sets, and let

$F\colon L\longrightarrow M$

be a mapping. Show that ${}F$ is surjective if and only if taking preimages

${\mathfrak {P}}\,(M)\longrightarrow {\mathfrak {P}}\,(L),T\longmapsto F^{-1}(T),$

is injective.

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