Answered: Consider the functions f : A → B, g : B…

Consider the functions f : A → B, g : B → A and h : B → A such that if gf = 1A and fh = 1B. Prove (a) f is a 1-1 correspondence A ∼ B. (b) f1A = f and 1Bf = f.

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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Question

Consider the functions f : A → B, g : B → A and h : B → A
such that if gf = 1A and fh = 1B.
Prove
(a) f is a 1-1 correspondence A ∼ B.
(b) f1A = f and 1Bf = f.

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