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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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