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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 |

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Discrete Mathematics With Applicat...

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

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Chapter
Section
BuyFindarrow_forward

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.

  1. 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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    Chapter 1 Solutions

    Discrete Mathematics With Applications
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