Ononot — Let f: X \to Y be a function, and let A and B be subsets of

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Set Theoryhard

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Let $f: X \to Y$ be a function, and let $A$ and $B$ be subsets of $Y$ . Consider the following statements regarding the preimage $f^{-1}$ : I. $f^{-1}(A \setminus B) = f^{-1}(A) \setminus f^{-1}(B)$ II. $f(f^{-1}(A)) = A$ III. $f^{-1}(A \cap B) = f^{-1}(A) \cap f^{-1}(B)$ Which of these statements must hold true for any function $f$ and any subsets $A, B \subseteq Y$ ?