a) Let $n$ $(n \geq 2)$ be an integer. On a line there are $n$ distinct (pairwise distinct) sets of points, such that for every integer $k$ $(1 \leq k \leq n)$ the union of every $k$ sets contains exactly $k+1$ points. Show that there is always a point that belongs to every set. b) Is the same conclusion true if there is an infinity of distinct sets of points such that for every positive integer $k$ the union of every $k$ sets contains exactly $k+1$ points?