Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 1.3, Problem 34WE

To determine

To explain:

The set of natural numbers is a field under addition and multiplication or not.

Expert Solution & Answer

Answer to Problem 34WE

The set of natural numbers is not a field under addition and multiplication because of the absence of Identity property of addition and property of opposites and property of reciprocals in multiplication.

Explanation of Solution

Definition of natural numbers:

Natural numbers are the numbers we use to count. They’re whole, non-negative numbers.

From the definition:

The set of natural numbers is not a field under addition, because the natural numbers does not obey the Identity property of addition and property of opposites.

The set of natural numbers is not a field under multiplication, because the natural numbers does not obey the property of reciprocals.

Chapter 1.3, Problem 33WE

Chapter 1.3, Problem 35WE

Chapter 1 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 1.1 - Prob. 1OE Ch. 1.1 - Prob. 2OE Ch. 1.1 - Prob. 3OE Ch. 1.1 - Prob. 4OE Ch. 1.1 - Prob. 5OE Ch. 1.1 - Prob. 6OE Ch. 1.1 - Prob. 7OE Ch. 1.1 - Prob. 8OE Ch. 1.1 - Prob. 9OE Ch. 1.1 - Prob. 10OE

Ch. 1.1 - Prob. 11OE Ch. 1.1 - Prob. 12OE Ch. 1.1 - Prob. 13OE Ch. 1.1 - Prob. 14OE Ch. 1.1 - Prob. 15OE Ch. 1.1 - Prob. 16OE Ch. 1.1 - Prob. 17OE Ch. 1.1 - Prob. 18OE Ch. 1.1 - Prob. 19OE Ch. 1.1 - Prob. 1WE Ch. 1.1 - Prob. 2WE Ch. 1.1 - Prob. 3WE Ch. 1.1 - Prob. 4WE Ch. 1.1 - Prob. 5WE Ch. 1.1 - Prob. 6WE Ch. 1.1 - Prob. 7WE Ch. 1.1 - Prob. 8WE Ch. 1.1 - Prob. 9WE Ch. 1.1 - Prob. 10WE Ch. 1.1 - Prob. 11WE Ch. 1.1 - Prob. 12WE Ch. 1.1 - Prob. 13WE Ch. 1.1 - Prob. 14WE Ch. 1.1 - Prob. 15WE Ch. 1.1 - Prob. 16WE Ch. 1.1 - Prob. 17WE Ch. 1.1 - Prob. 18WE Ch. 1.1 - Prob. 19WE Ch. 1.1 - Prob. 20WE Ch. 1.1 - Prob. 21WE Ch. 1.1 - Prob. 22WE Ch. 1.1 - Prob. 23WE Ch. 1.1 - Prob. 24WE Ch. 1.1 - Prob. 25WE Ch. 1.1 - Prob. 26WE Ch. 1.1 - Prob. 27WE Ch. 1.1 - Prob. 28WE Ch. 1.1 - Prob. 29WE Ch. 1.1 - Prob. 30WE Ch. 1.1 - Prob. 31WE Ch. 1.1 - Prob. 32WE Ch. 1.1 - Prob. 33WE Ch. 1.1 - Prob. 34WE Ch. 1.1 - Prob. 35WE Ch. 1.1 - Prob. 36WE Ch. 1.1 - Prob. 37WE Ch. 1.1 - Prob. 38WE Ch. 1.1 - Prob. 39WE Ch. 1.1 - Prob. 40WE Ch. 1.1 - Prob. 1MRE Ch. 1.1 - Prob. 2MRE Ch. 1.1 - Prob. 3MRE Ch. 1.1 - Prob. 4MRE Ch. 1.1 - Prob. 5MRE Ch. 1.1 - Prob. 6MRE Ch. 1.1 - Prob. 7MRE Ch. 1.1 - Prob. 8MRE Ch. 1.1 - Prob. 9MRE Ch. 1.1 - Prob. 10MRE Ch. 1.1 - Prob. 11MRE Ch. 1.1 - Prob. 12MRE Ch. 1.1 - Prob. 1CE Ch. 1.1 - Prob. 2CE Ch. 1.1 - Prob. 3CE Ch. 1.1 - Prob. 4CE Ch. 1.2 - Prob. 1OE Ch. 1.2 - Prob. 2OE Ch. 1.2 - Prob. 3OE Ch. 1.2 - Prob. 4OE Ch. 1.2 - Prob. 5OE Ch. 1.2 - Prob. 6OE Ch. 1.2 - Prob. 7OE Ch. 1.2 - Prob. 8OE Ch. 1.2 - Prob. 9OE Ch. 1.2 - Prob. 10OE Ch. 1.2 - Prob. 11OE Ch. 1.2 - Prob. 12OE Ch. 1.2 - Prob. 13OE Ch. 1.2 - Prob. 14OE Ch. 1.2 - Prob. 15OE Ch. 1.2 - Prob. 16OE Ch. 1.2 - Prob. 17OE Ch. 1.2 - Prob. 18OE Ch. 1.2 - Prob. 19OE Ch. 1.2 - Prob. 20OE Ch. 1.2 - Prob. 21OE Ch. 1.2 - Prob. 22OE Ch. 1.2 - Prob. 23OE Ch. 1.2 - Prob. 24OE Ch. 1.2 - Prob. 1WE Ch. 1.2 - Prob. 2WE Ch. 1.2 - Prob. 3WE Ch. 1.2 - Prob. 4WE Ch. 1.2 - Prob. 5WE Ch. 1.2 - Prob. 6WE Ch. 1.2 - Prob. 7WE Ch. 1.2 - Prob. 8WE Ch. 1.2 - Prob. 9WE Ch. 1.2 - Prob. 10WE Ch. 1.2 - Prob. 11WE Ch. 1.2 - Prob. 12WE Ch. 1.2 - Prob. 13WE Ch. 1.2 - Prob. 14WE Ch. 1.2 - Prob. 15WE Ch. 1.2 - Prob. 16WE Ch. 1.2 - Prob. 17WE Ch. 1.2 - Prob. 18WE Ch. 1.2 - Prob. 19WE Ch. 1.2 - Prob. 20WE Ch. 1.2 - Prob. 21WE Ch. 1.2 - Prob. 22WE Ch. 1.2 - Prob. 23WE Ch. 1.2 - Prob. 24WE Ch. 1.2 - Prob. 25WE Ch. 1.2 - Prob. 26WE Ch. 1.2 - Prob. 27WE Ch. 1.2 - Prob. 28WE Ch. 1.2 - Prob. 29WE Ch. 1.2 - Prob. 30WE Ch. 1.2 - Prob. 31WE Ch. 1.2 - Prob. 32WE Ch. 1.2 - Prob. 33WE Ch. 1.2 - Prob. 34WE Ch. 1.2 - Prob. 35WE Ch. 1.2 - Prob. 36WE Ch. 1.2 - Prob. 37WE Ch. 1.2 - Prob. 38WE Ch. 1.2 - Prob. 39WE Ch. 1.2 - Prob. 40WE Ch. 1.2 - Prob. 41WE Ch. 1.2 - Prob. 42WE Ch. 1.2 - Prob. 43WE Ch. 1.2 - Prob. 44WE Ch. 1.2 - Prob. 45WE Ch. 1.2 - Prob. 46WE Ch. 1.2 - Prob. 47WE Ch. 1.2 - Prob. 48WE Ch. 1.2 - Prob. 49WE Ch. 1.2 - Prob. 50WE Ch. 1.2 - Prob. 51WE Ch. 1.2 - Prob. 52WE Ch. 1.2 - Prob. 53WE Ch. 1.2 - Prob. 54WE Ch. 1.2 - Prob. 1ST Ch. 1.2 - Prob. 2ST Ch. 1.2 - Prob. 3ST Ch. 1.2 - Prob. 4ST Ch. 1.2 - Prob. 5ST Ch. 1.2 - Prob. 6ST Ch. 1.2 - Prob. 7ST Ch. 1.2 - Prob. 8ST Ch. 1.2 - Prob. 9ST Ch. 1.2 - Prob. 10ST Ch. 1.3 - Prob. 1OE Ch. 1.3 - Prob. 2OE Ch. 1.3 - Prob. 3OE Ch. 1.3 - Prob. 4OE Ch. 1.3 - Prob. 5OE Ch. 1.3 - Prob. 6OE Ch. 1.3 - Prob. 7OE Ch. 1.3 - Prob. 8OE Ch. 1.3 - Prob. 9OE Ch. 1.3 - Prob. 10OE Ch. 1.3 - Prob. 11OE Ch. 1.3 - Prob. 12OE Ch. 1.3 - Prob. 13OE Ch. 1.3 - Prob. 14OE Ch. 1.3 - Prob. 15OE Ch. 1.3 - Prob. 16OE Ch. 1.3 - Prob. 17OE Ch. 1.3 - Prob. 18OE Ch. 1.3 - Prob. 19OE Ch. 1.3 - Prob. 20OE Ch. 1.3 - Prob. 21OE Ch. 1.3 - Prob. 22OE Ch. 1.3 - Prob. 23OE Ch. 1.3 - Prob. 24OE Ch. 1.3 - Prob. 1WE Ch. 1.3 - Prob. 2WE Ch. 1.3 - Prob. 3WE Ch. 1.3 - Prob. 4WE Ch. 1.3 - Prob. 5WE Ch. 1.3 - Prob. 6WE Ch. 1.3 - Prob. 7WE Ch. 1.3 - Prob. 8WE Ch. 1.3 - Prob. 9WE Ch. 1.3 - Prob. 10WE Ch. 1.3 - Prob. 11WE Ch. 1.3 - Prob. 12WE Ch. 1.3 - Prob. 13WE Ch. 1.3 - Prob. 14WE Ch. 1.3 - Prob. 15WE Ch. 1.3 - Prob. 16WE Ch. 1.3 - Prob. 17WE Ch. 1.3 - 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Prob. 16OE Ch. 1.4 - Prob. 17OE Ch. 1.4 - Prob. 18OE Ch. 1.4 - Prob. 19OE Ch. 1.4 - Prob. 20OE Ch. 1.4 - Prob. 21OE Ch. 1.4 - Prob. 22OE Ch. 1.4 - Prob. 23OE Ch. 1.4 - Prob. 24OE Ch. 1.4 - Prob. 25OE Ch. 1.4 - Prob. 26OE Ch. 1.4 - Prob. 27OE Ch. 1.4 - Prob. 28OE Ch. 1.4 - Prob. 29OE Ch. 1.4 - Prob. 1WE Ch. 1.4 - Prob. 2WE Ch. 1.4 - Prob. 3WE Ch. 1.4 - Prob. 4WE Ch. 1.4 - Prob. 5WE Ch. 1.4 - Prob. 6WE Ch. 1.4 - Prob. 7WE Ch. 1.4 - Prob. 8WE Ch. 1.4 - Prob. 9WE Ch. 1.4 - Prob. 10WE Ch. 1.4 - Prob. 11WE Ch. 1.4 - Prob. 12WE Ch. 1.4 - Prob. 13WE Ch. 1.4 - Prob. 14WE Ch. 1.4 - Prob. 15WE Ch. 1.4 - Prob. 16WE Ch. 1.4 - Prob. 17WE Ch. 1.4 - Prob. 18WE Ch. 1.4 - Prob. 19WE Ch. 1.4 - Prob. 20WE Ch. 1.4 - Prob. 21WE Ch. 1.4 - Prob. 22WE Ch. 1.4 - Prob. 23WE Ch. 1.4 - Prob. 24WE Ch. 1.4 - Prob. 25WE Ch. 1.4 - Prob. 26WE Ch. 1.4 - Prob. 27WE Ch. 1.4 - Prob. 28WE Ch. 1.4 - Prob. 29WE Ch. 1.4 - Prob. 30WE Ch. 1.4 - Prob. 31WE Ch. 1.4 - Prob. 32WE Ch. 1.4 - Prob. 33WE Ch. 1.4 - Prob. 34WE Ch. 1.4 - Prob. 35WE Ch. 1.4 - Prob. 36WE Ch. 1.4 - Prob. 37WE Ch. 1.4 - Prob. 38WE Ch. 1.4 - Prob. 39WE Ch. 1.4 - Prob. 40WE Ch. 1.4 - Prob. 41WE Ch. 1.4 - Prob. 42WE Ch. 1.4 - Prob. 43WE Ch. 1.4 - Prob. 44WE Ch. 1.4 - Prob. 45WE Ch. 1.4 - Prob. 46WE Ch. 1.4 - Prob. 47WE Ch. 1.4 - Prob. 48WE Ch. 1.4 - Prob. 49WE Ch. 1.4 - Prob. 50WE Ch. 1.4 - Prob. 51WE Ch. 1.4 - Prob. 52WE Ch. 1.4 - Prob. 53WE Ch. 1.4 - Prob. 54WE Ch. 1.4 - Prob. 55WE Ch. 1.4 - Prob. 56WE Ch. 1.4 - Prob. 1E Ch. 1.4 - Prob. 2E Ch. 1.4 - Prob. 3E Ch. 1.4 - Prob. 4E Ch. 1.4 - Prob. 5E Ch. 1.4 - Prob. 6E Ch. 1.4 - Prob. 7E Ch. 1.5 - Prob. 1OE Ch. 1.5 - Prob. 2OE Ch. 1.5 - Prob. 3OE Ch. 1.5 - Prob. 4OE Ch. 1.5 - Prob. 5OE Ch. 1.5 - Prob. 6OE Ch. 1.5 - Prob. 7OE Ch. 1.5 - Prob. 8OE Ch. 1.5 - Prob. 9OE Ch. 1.5 - Prob. 10OE Ch. 1.5 - Prob. 11OE Ch. 1.5 - Prob. 12OE Ch. 1.5 - Prob. 13OE Ch. 1.5 - Prob. 14OE Ch. 1.5 - Prob. 15OE Ch. 1.5 - Prob. 16OE Ch. 1.5 - Prob. 17OE Ch. 1.5 - Prob. 18OE Ch. 1.5 - Prob. 19OE Ch. 1.5 - Prob. 20OE Ch. 1.5 - Prob. 1WE Ch. 1.5 - Prob. 2WE Ch. 1.5 - Prob. 3WE Ch. 1.5 - Prob. 4WE Ch. 1.5 - Prob. 5WE Ch. 1.5 - Prob. 6WE Ch. 1.5 - Prob. 7WE Ch. 1.5 - Prob. 8WE Ch. 1.5 - Prob. 9WE Ch. 1.5 - Prob. 10WE Ch. 1.5 - Prob. 11WE Ch. 1.5 - Prob. 12WE Ch. 1.5 - Prob. 13WE Ch. 1.5 - Prob. 14WE Ch. 1.5 - Prob. 15WE Ch. 1.5 - Prob. 16WE Ch. 1.5 - Prob. 17WE Ch. 1.5 - Prob. 18WE Ch. 1.5 - Prob. 19WE Ch. 1.5 - Prob. 20WE Ch. 1.5 - Prob. 21WE Ch. 1.5 - Prob. 22WE Ch. 1.5 - Prob. 23WE Ch. 1.5 - Prob. 24WE Ch. 1.5 - Prob. 25WE Ch. 1.5 - Prob. 26WE Ch. 1.5 - Prob. 27WE Ch. 1.5 - Prob. 28WE Ch. 1.5 - Prob. 29WE Ch. 1.5 - Prob. 30WE Ch. 1.5 - Prob. 31WE Ch. 1.5 - Prob. 32WE Ch. 1.5 - Prob. 33WE Ch. 1.5 - Prob. 34WE Ch. 1.5 - Prob. 35WE Ch. 1.5 - Prob. 36WE Ch. 1.5 - Prob. 1MRE Ch. 1.5 - Prob. 2MRE Ch. 1.5 - Prob. 3MRE Ch. 1.5 - Prob. 4MRE Ch. 1.5 - Prob. 5MRE Ch. 1.5 - Prob. 6MRE Ch. 1.5 - Prob. 7MRE Ch. 1.5 - Prob. 8MRE Ch. 1.5 - Prob. 9MRE Ch. 1.5 - Prob. 10MRE Ch. 1.5 - Prob. 11MRE Ch. 1.5 - Prob. 12MRE Ch. 1.5 - Prob. 1CE Ch. 1.5 - Prob. 2CE Ch. 1.5 - Prob. 3CE Ch. 1.5 - Prob. 4CE Ch. 1.6 - Prob. 1OE Ch. 1.6 - Prob. 2OE Ch. 1.6 - Prob. 3OE Ch. 1.6 - Prob. 4OE Ch. 1.6 - Prob. 5OE Ch. 1.6 - Prob. 6OE Ch. 1.6 - Prob. 7OE Ch. 1.6 - Prob. 8OE Ch. 1.6 - Prob. 9OE Ch. 1.6 - Prob. 10OE Ch. 1.6 - Prob. 11OE Ch. 1.6 - Prob. 12OE Ch. 1.6 - Prob. 13OE Ch. 1.6 - Prob. 14OE Ch. 1.6 - Prob. 15OE Ch. 1.6 - Prob. 16OE Ch. 1.6 - Prob. 17OE Ch. 1.6 - Prob. 18OE Ch. 1.6 - Prob. 19OE Ch. 1.6 - Prob. 1WE Ch. 1.6 - Prob. 2WE Ch. 1.6 - Prob. 3WE Ch. 1.6 - Prob. 4WE Ch. 1.6 - Prob. 5WE Ch. 1.6 - Prob. 6WE Ch. 1.6 - Prob. 7WE Ch. 1.6 - Prob. 8WE Ch. 1.6 - Prob. 9WE Ch. 1.6 - Prob. 10WE Ch. 1.6 - Prob. 11WE Ch. 1.6 - Prob. 12WE Ch. 1.6 - Prob. 13WE Ch. 1.6 - Prob. 14WE Ch. 1.6 - Prob. 15WE Ch. 1.6 - Prob. 16WE Ch. 1.6 - Prob. 17WE Ch. 1.6 - Prob. 18WE Ch. 1.6 - Prob. 19WE Ch. 1.6 - Prob. 20WE Ch. 1.6 - Prob. 21WE Ch. 1.6 - Prob. 22WE Ch. 1.6 - Prob. 23WE Ch. 1.6 - Prob. 24WE Ch. 1.6 - Prob. 25WE Ch. 1.6 - Prob. 26WE Ch. 1.6 - Prob. 27WE Ch. 1.6 - 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Prob. 17WE Ch. 1.7 - Prob. 18WE Ch. 1.7 - Prob. 19WE Ch. 1.7 - Prob. 20WE Ch. 1.7 - Prob. 21WE Ch. 1.7 - Prob. 22WE Ch. 1.7 - Prob. 23WE Ch. 1.7 - Prob. 24WE Ch. 1.7 - Prob. 25WE Ch. 1.7 - Prob. 26WE Ch. 1.7 - Prob. 27WE Ch. 1.7 - Prob. 28WE Ch. 1.7 - Prob. 29WE Ch. 1.7 - Prob. 30WE Ch. 1.7 - Prob. 31WE Ch. 1.7 - Prob. 32WE Ch. 1.7 - Prob. 33WE Ch. 1.7 - Prob. 34WE Ch. 1.7 - Prob. 35WE Ch. 1.7 - Prob. 36WE Ch. 1.7 - Prob. 37WE Ch. 1.7 - Prob. 38WE Ch. 1.7 - Prob. 39WE Ch. 1.7 - Prob. 40WE Ch. 1.7 - Prob. 41WE Ch. 1.7 - Prob. 42WE Ch. 1.7 - Prob. 43WE Ch. 1.7 - Prob. 44WE Ch. 1.7 - Prob. 45WE Ch. 1.7 - Prob. 46WE Ch. 1.7 - Prob. 47WE Ch. 1.7 - Prob. 48WE Ch. 1.7 - Prob. 49WE Ch. 1.7 - Prob. 50WE Ch. 1.7 - Prob. 51WE Ch. 1.7 - Prob. 52WE Ch. 1.7 - Prob. 53WE Ch. 1.7 - Prob. 1MRE Ch. 1.7 - Prob. 2MRE Ch. 1.7 - Prob. 3MRE Ch. 1.7 - Prob. 4MRE Ch. 1.7 - Prob. 5MRE Ch. 1.7 - Prob. 6MRE Ch. 1.7 - Prob. 7MRE Ch. 1.7 - Prob. 8MRE Ch. 1.7 - Prob. 9MRE Ch. 1.7 - Prob. 10MRE Ch. 1.7 - Prob. 11MRE Ch. 1.7 - 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Prob. 14CR Ch. 1 - Prob. 15CR Ch. 1 - Prob. 16CR Ch. 1 - Prob. 17CR Ch. 1 - Prob. 18CR Ch. 1 - Prob. 1CT Ch. 1 - Prob. 2CT Ch. 1 - Prob. 3CT Ch. 1 - Prob. 4CT Ch. 1 - Prob. 5CT Ch. 1 - Prob. 6CT Ch. 1 - Prob. 7CT Ch. 1 - Prob. 8CT Ch. 1 - Prob. 9CT Ch. 1 - Prob. 10CT Ch. 1 - Prob. 11CT Ch. 1 - Prob. 12CT Ch. 1 - Prob. 13CT Ch. 1 - Prob. 14CT Ch. 1 - Prob. 15CT Ch. 1 - Prob. 16CT Ch. 1 - Prob. 17CT

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The set of natural numbers is a field under addition and multiplication or not.

Videos

To explain: The set of natural numbers is a field under addition and multiplication or not.

Answer to Problem 34WE

Explanation of Solution

Chapter 1 Solutions

Additional Math Textbook Solutions

To explain:

The set of natural numbers is a field under addition and multiplication or not.