3/12/15

Let S be a set with 2002 elements, and let N be an integer with 0<N<2^2012. Prove that it is possible to color every subset of S either blue or red so that the following conditions hold:

(a) the union of any two red subsets is red;

(b) the union of any two blue subsets is blue;

(c) there are exactly N red subsets.

Hint: Use Induction

Level: 5