Exercise 4, § 6

Let S, T be two finite sets in $\mathbf{R}^n$, without common points, such that their union contains at least $2n + 2$ points. Then there exists a hyperplane separating S from T if, and only if, for every finite set $F \subset S \cup T$ of $2n + 2$ points, there exists a hyperplane separating $F \cap S$ from $F \cap T$ (use exerc. 3 and the method of II, p. 78, exerc. 15).