Answered: Let A, B, X, and Y be nonempty sets.…

Let A, B, X, and Y be nonempty sets. Prove/disprove the following statement. Let f : X → Y . If A ⊆ X, B ⊆ Y , and f^−1[B] = {x ∈ X|f(x) ∈ B}, then f[A] ∩ B = f[A ∩ f^−1[B]].

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let A, B, X, and Y be nonempty sets. Prove/disprove the following statement. Let f : X → Y . If A ⊆ X, B ⊆ Y , and f^−1[B] = {x ∈ X|f(x) ∈ B}, then f[A] ∩ B = f[A ∩ f^−1[B]].

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