Answer
See explanation
Work Step by Step
When we say “\(A\) has the same cardinality as \(B\),” we mean **there exists** a bijection (a one‐to‐one and onto function) from \(A\) **onto** \(B\). In other words, there is a function \(f : A \to B\) that is both injective and surjective.
The student’s reply—“\(A\) and \(B\) are one‐to‐one and onto”—misstates it as though the *sets themselves* were “one‐to‐one and onto,” rather than saying there is a *function* between them that is. The correct statement should be:
“There is a one‐to‐one and onto **function** \(f : A \to B\).”
