f : A → B and g : B → C are functions such that g ◦ f is surjective, then f is surjective. (ii) If f : A → B and g : B → C are functions
f : A → B and g : B → C are functions such that g ◦ f is surjective, then f is surjective. (ii) If f : A → B and g : B → C are functions
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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We have shown that the composition of two surjective functions is surjective, i.e. that if f : A → B and g : B → C are surjective, then g◦f : A → C is surjective. Now decide whether the following statements are true or false, and prove your claim. Remember, to prove that a statement is wrong, all you need to do is to give a counterexample.
(i) If f : A → B and g : B → C are functions such that g ◦ f is surjective, then f is surjective.
(ii) If f : A → B and g : B → C are functions such that g ◦ f is surjective, then g is surjective.
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