Let $f: X \rightarrow Y$ be a function and $A, B$ be non-void subsets of $Y$. Which of the following is true?

  • A
    $f^{-1}(A) - f^{-1}(B) \supset f^{-1}(A - B)$ but the opposite does not hold.
  • B
    $f^{-1}(A) - f^{-1}(B) \subset f^{-1}(A - B)$ but the opposite does not hold.
  • C
    $f^{-1}(A - B) = f^{-1}(A) - f^{-1}(B)$
  • D
    $f^{-1}(A - B) = f^{-1}(A) \cup f^{-1}(B)$

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