In this problem, we will deal with subsets AS R. Here, N= {0, 1, 2,...}. Let's define two new concepts. (i) We say that A is naturally increasing if VxE A, 3y € A s.t. x+y AND y-xEN (ii) We say that A is spottily decreasing if 3x € A s.t. Vy € A,x-y EN Below are six claims. Which ones are true and which ones are false? If a claim is true, prove it. If a claim is false, provide a counterexample and a justification of how the counterexample shows the claim is false. Hint: can you find a set A such that A is naturally increasing? can you find a set B such that B is spottily decreasing? (a) If A is spottily decreasing, then A is naturally increasing. This statement is O True O False 已保存 (b) If A is naturally increasing, then A is not spottily decreasing. This statement is O True O False (c) If A is not naturally increasing, then A is spottily decreasing. This statement is O True O False