MathDB

Given

S

be the finite lattice (with integer coordinate) set in the

xy

-plane.

A

is the subset of

S

with most elements such that the line connecting any two points in

A

is not parallel to

x

-axis or

y

-axis.

B

is the subset of integer with least elements such that for any

(x,y)\in S

x \in B

y \in B

holds. Prove that

|A| \geq |B|

Problem Statement