   # Rewrite the following statements less formally, Without using variables. Determine, as best as you can, whether the statements are true or fales. There are real numbers u and v with the property that u + v &lt; u − v . There is a real number x such that x 2 &lt; x . For every positive integer n , n 2 ≥ n . For all real numbers a and b , | a + b | ≤ | a | + | b | ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193
Chapter 1.1, Problem 7ES
Textbook Problem
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## Rewrite the following statements less formally, Without using variables. Determine, as best as you can, whether the statements are true or fales. There are real numbers u and v with the property that u + v < u − v . There is a real number x such that x 2 < x .For every positive integer n , n 2 ≥ n .For all real numbers a and b , | a + b | ≤ | a | + | b |

To determine

(a)

That the statement is true or false and to rewrite the given statement: There are real numbers u and v with property that u + v < u − v.

### Explanation of Solution

Given:

Statement: There are real numbers u and v with property that u + v < u − v.

Thus, the statement can be rewritten as: there are real numbers whose sum is less than their difference...

To determine

(b)

That the statement is true or false and to rewrite the given statement: There is a real number x such that x2<x.

To determine

(c)

That the statement is true or false and to rewrite the given statement: For every positive integer n, n2n.

To determine

(d)

That the statement is true or false and to rewrite the given statement: For all real numbers a and b, |a+b||a|+|b|.

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