Ononot — Let f: X \to Y be a function. For any subsets A, B \subseteq

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Set Theoryhard

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Let $f: X \to Y$ be a function. For any subsets $A, B \subseteq X$ , let $f(A)$ denote the image of $A$ under $f$ . Which of the following conditions on $f$ is both necessary and sufficient for the identity $f(A \cap B) = f(A) \cap f(B)$ to hold for all subsets $A, B \subseteq X$ ?