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 )

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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. 

  1. ∃x ( x2 - 4 > 0 )
  2. ∀x( x2 - 4 > 0 )
  3. ∃x ( x ≤ x2 )
  4. ∀x ( x ≤ x2 )
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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 )

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