Skip to main content\( \newcommand{\identity}{\mathrm{id}}
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Chapter 8 Injections and Surjections
Let \(X,Y,Z\) be finite sets, perhaps of different sizes. Let \(f:X \rightarrow Y\) and \(g:Y \rightarrow Z\text{.}\) Decide whether each of the following statements is true or false.
If the statement is true, provide a proof. (It will be easier to prove the contrapositive.)
If the statement is false, provide a counterexample.
Exercises Practice Problems
1.
If \(g \circ f\) is injective then \(f\) is injective.
2.
If \(g \circ f\) is injective then \(g\) is injective.
3.
If \(g \circ f\) is surjective then \(f\) is surjective.
4.
If \(g \circ f\) is surjective then \(g\) is surjective.