#T. Prove that the following two statements are not logically equivalent. In your proof, completely justify your answer. (a) A real number is less than 1 only if its reciprocal is greater than 1. (b) Having a reciprocal greater than 1 is a sufficient condition for a real number to be less than 1.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 40E
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#1.
Prove that the following two statements are not logically equivalent. In your
proof, completely justify your answer.
(a) A real number is less than 1 only if its reciprocal is greater than 1.
(b) Having a reciprocal greater than 1 is a sufficient condition for a real
number to be less than 1.
Transcribed Image Text:#1. Prove that the following two statements are not logically equivalent. In your proof, completely justify your answer. (a) A real number is less than 1 only if its reciprocal is greater than 1. (b) Having a reciprocal greater than 1 is a sufficient condition for a real number to be less than 1.
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