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Answered Same Day Dec 23, 2021

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Robert answered on Dec 23 2021

136 Votes

Suppose f is surjective: We will prove for every X ⊂ A,
f(Xc) = (f(X))c
Let b ∈ f(Xc), that is there is some a ∈ Xc such that b = f(a). If b /∈
(f(X))c then we must have b ∈ f(X), this means there must exists some a2 ∈
X such that b = f(a2). But we have b = f(a). But this is not possible
ecause a ∈ Xc and...

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