GATE CS 2014 Set 3 — Question 12
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Engineering Mathematics → Sets & Combinatorics → Sets, Relations & Functions
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Question
Let and be finite sets and be a function. Which one of the following statements is TRUE?
Correct answer
(D) For any subsets S and T of Y, f⁻¹(S ∩ T) = f⁻¹(S) ∩ f⁻¹(T)
Solution
Let's analyze the options:(A) : This is false. Generally, . Equality holds only if and are disjoint.(B) : This is false. The correct property is . Equality holds if is injective.(C) : This is false. Since , the size is bounded by the intersection size, but not necessarily the minimum of the image sizes.(D) : This is true. The inverse image of an intersection is the intersection of the inverse images.
Proof: .
Proof: .
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