WBJEE · Maths · Sets and Relations
Let \(f: X \rightarrow Y\) and \(A, B\) are non-void subsets of \(Y\), then (where the symbols have their usual interpretation)
- 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 \(f^{-1}(A-B)=f^{-1}(A) \cup f^{-1}(B)\)
Answer & Solution
Correct Answer
(C) \(f^{-1}(A-B)=f^{-1}(A)-f^{-1}(B)\)
Step-by-step Solution
Detailed explanation
Let A={1,2,3} and B={2,3,4} here, \(f^{-1}(3)=1\) \(f^{-1}(4)=2\) and \(f^{-1}(2)=3\) It is clear that option (C) \(f^{-1}(A-B)=f^{-1}(A)\) \(-f^{-1}(B)\) is correct.
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