We are given an infinite set of rectangles in the plane, where each rectangle has vertices of the form \((0,0), (n,0), (0,m) (n,m)\) for positive integers \(m\) and \(n\) (\(m\) and \(n\) vary from rectangle to rectangle).

(a) Prove that there exist two rectangles in the set such that one contains the other.

(b) * Prove or disprove: there must exist an infinite sequence \(R_1,R_2,\ldots,R_n,\ldots\) of rectangles in the set such that \(R_1\) is contained in \(R_2\), \(R_2\) is contained in \(R_3\), and so on. (\(R_i\) is contained in \(R_{i+1}\) for each \(i\)).