Prove the following statement directly from the definition of rational number. The difference of any two rational numbers is a rational number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r = and s = a I,r%3D for some --Select-- v a, b, c, and d with ---Select--- Write r-s in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following. r-s = Both the numerator and the denominator are integers because---Select--- In addition, bd # 0 by the -Select---

Prove the following statement directly from the definition of rational number. The difference of any two rational numbers is a rational number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r = and s = a I,r%3D for some --Select-- v a, b, c, and d with ---Select--- Write r-s in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following. r-s = Both the numerator and the denominator are integers because---Select--- In addition, bd # 0 by the -Select---

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.4: Binary Operations

Problem 12E

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