Suppose f: X→Y, and A, B CY. Prove that (a) f-¹(AUB) = ƒ−¹(A) U ƒ−¹(B). (b) f-¹(ANB) = f¯¹(A) n f¯¹(B).
Suppose f: X→Y, and A, B CY. Prove that (a) f-¹(AUB) = ƒ−¹(A) U ƒ−¹(B). (b) f-¹(ANB) = f¯¹(A) n 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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b)
Transcribed Image Text:Suppose \( f: X \to Y \), and \( A, B \subseteq Y \). Prove that
(a) \( f^{-1}(A \cup B) = f^{-1}(A) \cup f^{-1}(B) \).
(b) \( f^{-1}(A \cap B) = f^{-1}(A) \cap f^{-1}(B) \).
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