3. Let f A → B be a function and let S be a subset of A. (i) Show that S c ƒ˜¹ (ƒ(S)). (ii) If f is one-to-one, show that S = ƒ−¹(ƒ(S)).
3. Let f A → B be a function and let S be a subset of A. (i) Show that S c ƒ˜¹ (ƒ(S)). (ii) If f is one-to-one, show that S = ƒ−¹(ƒ(S)).
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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proof question
please see the picture , thanks.
Let f : A ! B be a function and let S be a subset of A.
(i) Show that S f?1(f(S)).
(ii) If f is one-to-one, show that S = f?1(f(S)).
![3. Let f: A B be a function and let S be a subset of A.
(i) Show that S ℃ ƒ−¹(ƒ(S)).
(ii) If ƒ is one-to-one, show that S = ƒ−¹(ƒ(S)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F979d0aba-5428-414f-a3ba-5510f0301082%2F8661643f-c1d8-48fd-a31a-982c0958afae%2F0keyfps_processed.png&w=3840&q=75)
Transcribed Image Text:3. Let f: A B be a function and let S be a subset of A.
(i) Show that S ℃ ƒ−¹(ƒ(S)).
(ii) If ƒ is one-to-one, show that S = ƒ−¹(ƒ(S)).
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