If $X$ and $Y$ are two non-empty sets where $f: X \to Y$ is a function defined such that $f(C) = \{f(x) : x \in C\}$ for $C \subseteq X$ and $f^{-1}(D) = \{x : f(x) \in D\}$ for $D \subseteq Y$,then for any $A \subseteq X$ and $B \subseteq Y$,which of the following is true?
- A$f^{-1}(f(A)) = A$
- B$f^{-1}(f(A)) = A$ only if $f$ is surjective
- C$f(f^{-1}(B)) = B$ only if $B \subseteq f(X)$
- D$f(f^{-1}(B)) = B$
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