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We have shown that the composition of two surjective functions is surjective, i.e. th if f : A → B and g : B → C are surjective, then go f : A → C is surjective. Now deci whether the following statements are true or false, and prove your claim. Remembe to prove that a statement is wrong, all you need to do is to give a counterexample. (i) If ƒ : A → B and g : B → C are functions such that go f is surjective, then f surjective. (ii) If f : A → B and g: B → C are functions such that go f is surjective, then 9 surjective. Get started by drawing some pictures of sets with arrows. No need to submit yo

We have shown that the composition of two surjective functions is surjective, i.e. th if f : A → B and g : B → C are surjective, then go f : A → C is surjective. Now deci whether the following statements are true or false, and prove your claim. Remembe to prove that a statement is wrong, all you need to do is to give a counterexample. (i) If ƒ : A → B and g : B → C are functions such that go f is surjective, then f surjective. (ii) If f : A → B and g: B → C are functions such that go f is surjective, then 9 surjective. Get started by drawing some pictures of sets with arrows. No need to submit yo

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.7: Combining Functions
Problem 4E: We can express the function in Exercise 3 algebraically as f(x)=g(x)= (fg)(x)=(gf)(x)=
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We have shown that the composition of two surjective functions is surjective, i.e. that if ƒ : A → B and g : B → C are surjective, then go 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 go f is surjective, then f is surjective. (ii) If f : A → B and g : B → C are functions such that go f is surjective, then g is surjective. Get started by drawing some pictures of sets with arrows. No need to submit your drawings.
Transcribed Image Text:We have shown that the composition of two surjective functions is surjective, i.e. that if ƒ : A → B and g : B → C are surjective, then go 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 go f is surjective, then f is surjective. (ii) If f : A → B and g : B → C are functions such that go f is surjective, then g is surjective. Get started by drawing some pictures of sets with arrows. No need to submit your drawings.
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