Past exam of the mathematics course of the University of Cambridge / 2002 / ia / Paper 4 / 1C / Solution

An injective function satisfies $f(a)=f(a^{\prime })\Rightarrow a=a^{\prime }$ for all $a,a^{\prime }\in A$. A surjective function $g:A\to B$ satisfies: for every $b\in B$, some $a\in A$ has $g(a)=b$. The following arguments apply to function composition with the stated domains and codomains.