Determine the truth value of the statements below if the domain of each variable consists of all real numbers. I would like to understand this better. Like for the first one, I would think that there is some real number that would make the statement true. ∃x ( x2 - 4 > 0 ) ∀x( x2 - 4 > 0 ) ∃x ( x ≤ x2 ) ∀x ( x ≤ x2 )

Determine the truth value of the statements below if the domain of each variable consists of all real numbers. I would like to understand this better. Like for the first one, I would think that there is some real number that would make the statement true. ∃x ( x2 - 4 > 0 ) ∀x( x2 - 4 > 0 ) ∃x ( x ≤ x2 ) ∀x ( x ≤ x2 )

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 64WE

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Question

Determine the truth value of the statements below if the domain of each variable consists of all real numbers.

I would like to understand this better. Like for the first one, I would think that there is some real number that would make the statement true.

∃x ( x² - 4 > 0 )
∀x( x² - 4 > 0 )
∃x ( x ≤ x² )
∀x ( x ≤ x² )

Expert Solution

Step 1

We have to determine the truth value of the statements (i.e., statement is true or false) below if the domain of each variable consists of all real numbers.

1. ∃x ( x² - 4 > 0 )

2. ∀x( x² - 4 > 0 )

3. ∃x ( x ≤ x² )

4. ∀x ( x ≤ x² )