Prove or provide a counterexample to the following statement: if f : A → B and g : B → C are functions such that go f is onto, then f is onto.

Q: (c) Show that if g o f is onto then g must be onto.

A: Solution:-

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Q: C. How many extensions of g to A are onto?

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A: Does not exists because f is not onto.

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A: Everything You have done was correct except the second last step . So, I m doing from there . Since…

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A: The function f:A→B, where A=ℤ×ℤ, B=ℤ×ℤ such that fx,y=y,x

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Q: Are f and g both necessarily onto, if gof is onto?

A: Given: f and g are two functions and gof is onto.

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A: Let  A be any we define a relation R on A s.t

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A: please see the next step for solution

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Q: Let g: A ---------- B andf: B-----------C. Prove that f is onto if f 0 g is onto.

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Q: (a) Prove that there exists a function f: Z → Z so that f is one-to-one but f is not onto. (b) Prove…

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Q: Let z be the set of integers and f:Z → Z be defined as f(x)=-4x+5. Then the inverse function of f *…

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Q: Let R be a relation on the set of all integers such that aRb if and only if a + b is even. Is R…

A:

Q: Let R be the relation defined on P({1,.…, 100}) by ... ARB if and only if |AUB| is even. Is R…

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Q: (a) Prove that there exists a function f : Z→ Z so that f is one-to-one but f is not onto. (b) Prove…

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Q: In question 3b, our proof uses the assumption that f is a bijection to argue that there exists an…

A: The answer will be,  f is onto (only)  Therefore the 1st option is correct.

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