\problemdata                                                             
        {Injection/Surjection} % latex-friendly label for the prob.
        {Injections/Surjections} % The topic(s) of the problem content.  
        {?} % Source (if known)                                          
        {S01 Tutorial 7, 2} % Usage (list ones you are aware of). 
        {Tina Wang, S02} % Last revision info (author, date).   
                                                                         
                                                                         
\begin{problem}           
Show that if there is a surjection from a set $A$ to a
set $B$, then there is an injection from $B$ to $A$.

\solution{
Take $f:A\rightarrow B$ a surjection. Then for each $b\in B$, we can
find $a\in A$ such that $f(a)=b$. For each $b\in B$, fix one such $a$
and let $g(b)=a$. $g:B\rightarrow A$ is an injection since if $g(b_1)=a$
and $g(b_2)=a$, then $f(a)=b_1$ and $f(a)=b_2$, so $b_1=b_2$ since $f$
is a function.
}
\end{problem}
                                 