Question 19
$P$ is a polygon. Its sides do not intersect except at its vertices, and no three vertices lie on a line. The pair of sides $AB$, $PQ$ is called special if (1) $AB$ and $PQ$ do not share a vertex and (2) either the line $AB$ intersects the segment $PQ$ or the line $PQ$ intersects the segment $AB$. Show that the number of special pairs is even.