AUSTRIAN-POLISH 1987 Problem 9

Let $M$ be the set of all points $(x,y)$ in the cartesian plane, with integer coordinates satisfying $1 \le x \le 12$ and $1 \le y \le 13$ . (a) Prove that every $49$ -element subset of $M$ contains four vertices of a rectangle with sides parallel to the coordinate axes. (b) Give an example of a $48$ -element subset of $M$ without this property.