Let $f: X \rightarrow Y$ be a function. If $P \subset X$ and $Q \subset Y$, define $f(P)=\{f(x): x \in P\}$ and $f^{-1}(Q)=\{x: f(x) \in Q\}$. Then the true statement/statements is/ are

• Correct answer
  A

  $f^{-1}(Q) \cap f^{-1}(R)=f^{-1}(Q \cap R)$
• B

  $f\left(f^{-1}(Q)\right)=Q$
• Correct answer
  C

  $f^{-1}(Q) \cup f^{-1}(R)=f^{-1}(Q \cup R)$
• D

  $f^{-1}(f(P))=P$

Hence, the correct answer is options: 'A', 'C'.