Question 5
Let $V$ be a finite subset of Euclidean space consisting of points $(x,y,z)$ with integer coordinates. Let $S_1,S_2,S_3$ be the projections of $V$ onto the $yz,xz,xy$ planes, respectively. Prove that
$$|V|^2\le |S_1||S_2||S_3|$$
($|X|$ denotes the number of elements of $X$).
$$|V|^2\le |S_1||S_2||S_3|$$
($|X|$ denotes the number of elements of $X$).