Assuming single-pion exchange in the reaction $\ensuremath{\pi}+p\ensuremath{\rightarrow}\ensuremath{\pi}+\ensuremath{\pi}+B$ where $B$ is the final-state baryon, we have calculated the total ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$, and ${\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ cross sections from the elastic scattering amplitude in the forward direction.