Claim: ACB if and only if An B = A. Proof. First, assume that AC B. We know, by a theorem in the textbook, that An BC A. To prove A CAN B, let's start with any * E [Select] ✓. Since ACB, € [Select] . Thus x E A and B. So, x EAN B, showing that A CAN B. Hence An B = A. Next, suppose AnB = A. Let x E A. Since (by hypothesis) An B = [Select] , An B. So, x € [Select] and B. Thus x € B. Hence ACB.

Claim: ACB if and only if An B = A. Proof. First, assume that AC B. We know, by a theorem in the textbook, that An BC A. To prove A CAN B, let's start with any * E [Select] ✓. Since ACB, € [Select] . Thus x E A and B. So, x EAN B, showing that A CAN B. Hence An B = A. Next, suppose AnB = A. Let x E A. Since (by hypothesis) An B = [Select] , An B. So, x € [Select] and B. Thus x € B. Hence ACB.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 87E

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