Let f : X → Y and A , B are non-void subsets of Y , then (where the symbols have their usual interpretation)

Question

Let f : X → Y and A , B are non-void subsets of Y , then (where the symbols have their usual interpretation), f − 1 ( A ) − f − 1 ( B ) ⊃ f − 1 ( A − B ) but the opposite does not hold., f − 1 ( A ) − f − 1 ( B ) ⊂ f − 1 ( A − B ) but the opposite does not hold., f − 1 ( A − B ) = f − 1 ( A ) − f − 1 ( B ), f − 1 ( A − B ) = f − 1 ( A ) ∪ f − 1 ( B )

MARKS App · Accepted Answer

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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