= Solution
Apply the preceding argument to $q+r$ to obtain a nonconstant <meromorphic function> $g$ with simple poles exactly at $q,r$. Both $f,g$, and the constant function one, belong to $L(p+q+r)$.
If $a+bf+cg=0$, examination at $p$, where only $f$ has a pole, forces $b=0$. Examination at $r$, where only $g$ has a pole, forces $c=0$, and then $a=0$. Thus the three functions are <linearly independent>. Since the <Riemann-Roch theorem> gives $\ell(p+q+r)=3$,
$$
\boxed{\{1,f,g\}\text{ is a basis of }L(p+q+r).}
$$
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