Let P(x) be the predicate “x > 1/x.” a) Write P(2), P( 1/2 ), P(−1), P(−1/2 ), and P(−8), and indicate which of these statements are true and which are false. b) Find the truth set of P(x) if the domain of x is R, the set of all real numbers. c) If the domain is the set R+ of all positive real numbers, what is the truth set of P(x)?

Let P(x) be the predicate “x > 1/x.” a) Write P(2), P( 1/2 ), P(−1), P(−1/2 ), and P(−8), and indicate which of these statements are true and which are false. b) Find the truth set of P(x) if the domain of x is R, the set of all real numbers. c) If the domain is the set R+ of all positive real numbers, what is the truth set of P(x)?

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter10: Inequalities

Section10.2: Solving Inequalities

Problem 62WE

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Question

Let P(x) be the predicate “x > 1/x.”
a) Write P(2), P( 1/2 ), P(−1), P(−1/2 ), and P(−8), and indicate which of these statements are
true and which are false.
b) Find the truth set of P(x) if the domain of x is R, the set of all real numbers.
c) If the domain is the set R+ of all positive real numbers, what is the truth set of P(x)?

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