ans following question with math proof style. Simple question for math major, should not take more than half hour.

math531_project.pdf

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MATH 531 PROJECT

This project is not mandatory. It will be used to add 10% to your second

exam score or replace your lowest quiz score (one that is not dropped). It is due

on April 15.

For each of the following either give a proof or provide a counterexample.

Suppose f : X ! Y and g : Y ! Z. To …nd counterexamples you can usually

let X and Y .be (maybe di¤erent) subsets of f1; 2; 3g :

1. If f is injective and g is injective, then g f is injective

2. If f is injective and g is injective, then g f is surjective

3. If f is injective and g is surjective, then g f is injective

4. If f is injective and g is surjective, then g f is surjective

5. If f is surjective and g is injective, then g f is injective

6. If f is surjective and g is injective, then g f is surjective

7. If f is surjective and g is surjective, then g f is injective

8. If f is surjective and g is surjective, then g f is surjective

9. If g f is injective, then f is injective

10. If g f is injective, then f is surjective

11. If g f is surjective, then g is injective

12. If g f is surjective, then g is surjective

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