Given two points (x0, y0) and (x1, y1) of ℝ2, defineif x0<x1 and y0 ≤ y1. Show that the...

Given two points (x0, y0) and (x1, y1) of ℝ2, define

if x0<x1 and y0 ≤ y1. Show that the curves y = x3 and y = 2 are maximal simply ordered subsets of ℝ2, and the curve y = x2 is not. Find all maximal simply ordered subsets.