1. In this problem, we will deal with subsets A C R. Let's define two new concepts. (i) We say that A is blow-up if 3x E A s.t. Vy E A,x - y > 0 = x - y is an odd integer. (ii) We say that A is step-down if Vx E A, By E A s.t. x - y _ 1 AND x - y is an even integer. (Part 1) To help you understand the definitions, here are two sets A = {-2, 0, 3, 3.5, 4} and B = {2k : ke Z}. (B) Prove that B is a step-down set by using the definition