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(a) If A is spottily decreasing, then A is naturally increasing. This statement is True False

(a) If A is spottily decreasing, then A is naturally increasing. This statement is True False

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 54E
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In this problem, we will deal with subsets A CR. Here, N = {0, 1, 2,...}. Let's define two new concepts. (i) We say that A is naturally increasing if Vr € A, ³y € A s.t. zy AND y - z EN (ii) We say that A is spottily decreasing if A s.t. Vy A,z-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?
Transcribed Image Text:In this problem, we will deal with subsets A CR. Here, N = {0, 1, 2,...}. Let's define two new concepts. (i) We say that A is naturally increasing if Vr € A, ³y € A s.t. zy AND y - z EN (ii) We say that A is spottily decreasing if A s.t. Vy A,z-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 True False
Transcribed Image Text:(a) If A is spottily decreasing, then A is naturally increasing. This statement is True False
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