Use the method of proof by contradiction to prove the following statements. a. Prove that the square root of 6 is irrational. b. Suppose a,b, and c are integers. If a^2 + b^2 = c^2, then a or b is even. c. For every positive x such that x is a rational number, there is a positive y such that y is a rational number for which y < x. d. If a and b are positive real numbers, then a + b is greater than or equal to 2 * SQRT(ab).
Use the method of proof by contradiction to prove the following statements. a. Prove that the square root of 6 is irrational. b. Suppose a,b, and c are integers. If a^2 + b^2 = c^2, then a or b is even. c. For every positive x such that x is a rational number, there is a positive y such that y is a rational number for which y < x. d. If a and b are positive real numbers, then a + b is greater than or equal to 2 * SQRT(ab).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 39E
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Use the method of proof by contradiction to prove the following statements.
a. Prove that the square root of 6 is irrational.
b. Suppose a,b, and c are integers. If a^2 + b^2 = c^2, then a or b is even.
c. For every positive x such that x is a rational number, there is a positive y such that y is a rational number for which y < x.
d. If a and b are positive real numbers, then a + b is greater than or equal to 2 * SQRT(ab).
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