Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Videos

Question

Chapter 1.3, Problem 31WE

(a)

To determine

To explain:

The set of rational numbers is closed under addition or not.

(a)

Expert Solution

Answer to Problem 31WE

The set is closed under addition.

Explanation of Solution

The members of the set are rational numbers.

Rational numbers are set of all real numbers ab , where a , and b are integer and b is not equal to zero.

Choose the members, 23 and 63 , find their sum.

23+63=83

The numbers 83 is a rational number since the denominator is not zero.

Thus, the set is closed under addition.

(b)

To determine

To explain:

The set of rational numbers is closed under multiplication or not.

(b)

Expert Solution

Answer to Problem 31WE

The set is closed under multiplication.

Explanation of Solution

Choose any two members from the set, 12 , and 8 , find their product.

12×8=82=4

Similarly, choose 34 , and 74 , find their product.

34×74=2116

The numbers 4 and 2116 are rational numbers, so they will be members of the set.

Therefore, the set is closed under multiplication.

Chapter 1.3, Problem 30WE

Chapter 1.3, Problem 32WE

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

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The set of rational numbers is closed under addition or not.

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To explain: The set of rational numbers is closed under addition or not.

Answer to Problem 31WE

Explanation of Solution

To explain: The set of rational numbers is closed under multiplication or not.

Answer to Problem 31WE

Explanation of Solution

Chapter 1 Solutions

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To explain:

The set of rational numbers is closed under addition or not.

To explain:

The set of rational numbers is closed under multiplication or not.