Let \(P\) be the family of partial injective functions from \(A\) to \(A\) ordered by extension, with \(A\) infinite. If a chain \(C\) has union \(f=\bigcup C\), what conclusion follows when applying Zorn's lemma?
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C. That \(f\in P\) is an upper bound of \(C\), and there is a maximal partial injection, whose domain and image are equal.
The union of a chain of partial injections is still injective, and a maximal one is a partial injection, i.e. a bijection between its domain and image.
Zorn's lemma is a principle equivalent to the axiom of choice stating that every nonempty partially ordered set in which every chain has an upper bound contains a maximal element.