For each of the following universal statements, indicate if the statement is true or false. If it is false, provide a specific value that represents a counterexample and show why it makes the statement false. [Note: For any number x, |x| represents the absolute value of x. For example, |7| = 7, | − 11| = 11, and |0| = 0.] (a) (∀n ∈ Z) (n > −3n) (b) (∀n ∈ Z) (|n| ≥ n) (c) (∀n ∈ Z) ( (n^2)/(n^2)+1) is not an integer). (d) (∀x ∈ R) ((x^2) ≥ 7x -10

For each of the following universal statements, indicate if the statement is true or false. If it is false, provide a specific value that represents a counterexample and show why it makes the statement false. [Note: For any number x, |x| represents the absolute value of x. For example, |7| = 7, | − 11| = 11, and |0| = 0.] (a) (∀n ∈ Z) (n > −3n) (b) (∀n ∈ Z) (|n| ≥ n) (c) (∀n ∈ Z) ( (n^2)/(n^2)+1) is not an integer). (d) (∀x ∈ R) ((x^2) ≥ 7x -10

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

For each of the following universal statements, indicate if the statement
is true or false. If it is false, provide a specific value that represents a counterexample and show why it makes the statement false.
[Note: For any number x, |x| represents the absolute value of x.
For example, |7| = 7, | − 11| = 11, and |0| = 0.]
(a) (∀n ∈ Z) (n > −3n)
(b) (∀n ∈ Z) (|n| ≥ n)
(c) (∀n ∈ Z) ( (n^2)/(n^2)+1) is not an integer).
(d) (∀x ∈ R) ((x^2) ≥ 7x -10)

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