a. Suppose that r E Q and x E Qº. Prove or disprove: The number (r – x)- E Q°. b. Prove or disprove. Given irrational numbers x, y E Qª, then their product xy E Q°. c. Prove that there is no rational number whose square is prime.

a. Suppose that r E Q and x E Qº. Prove or disprove: The number (r – x)- E Q°. b. Prove or disprove. Given irrational numbers x, y E Qª, then their product xy E Q°. c. Prove that there is no rational number whose square is prime.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 37E

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Question

a. Suppose that r E Q and x E Qº. Prove or disprove: The number (r – x)-1 E Q°.
b. Prove or disprove. Given irrational numbers x, y E Qª, then their product xy E Q°.
c. Prove that there is no rational number whose square is prime.

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