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Let f : A → B be a function. Prove the following: (a) If f is injective, then f is surjective. (b) If ƒ is surjective, f then is injective.

Let f : A → B be a function. Prove the following: (a) If f is injective, then f is surjective. (b) If ƒ is surjective, f then is injective.

Advanced Engineering Mathematics
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 f : A → B be a function. Prove the following: (a) If f is injective, then f is surjective. (b) If f is surjective, f then is injective.
Transcribed Image Text:Let f : A → B be a function. Prove the following: (a) If f is injective, then f is surjective. (b) If f is surjective, f then is injective.
Let f: A→ B be a function. If D is any subset of B, the inverse image of D under f, which we write f (D), is the following subset of A: Š (D) = {r € A|f (x) E D} . %3D That is, f (D) is the set of all the pre-images of the elements of D.
Transcribed Image Text:Let f: A→ B be a function. If D is any subset of B, the inverse image of D under f, which we write f (D), is the following subset of A: Š (D) = {r € A|f (x) E D} . %3D That is, f (D) is the set of all the pre-images of the elements of D.
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