   Chapter 3.1, Problem 4E

Chapter
Section
Textbook Problem
1 views

# In Exercises 1 − 14 , decide whether each of the given sets is a group with respect to the indicated operation. If it is not a group, state a condition in Definition 3.1 that fails to hold.The set ℚ ′ of all irrational numbers with operation addition.

To determine

Whether the set ' of all irrational numbers is a group with operation addition.

Explanation

Given information:

The set ' of all irrational numbers with operation addition.

Explanation:

Let us check that the set of all irrational numbers with operation addition is a group or not by using the definition given below:

Suppose the binary operation is defined for element of a set G. The set G is a group with respect to , provided the following conditions hold:

1. G is closed under . That is xG and yG imply that xy is in G.

2. is associative. For all x,y,z in G, x(yz)=(xy)z.

3. G has an identity element e. There is an e in G such that xe=ex=x for all xG

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Expand each expression in Exercises 122. (xx2)(x+x2)

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Evaluate the integral, if it exists. 04x1dx

Single Variable Calculus: Early Transcendentals, Volume I

#### Graphing Inequalities 12. x 1

Precalculus: Mathematics for Calculus (Standalone Book)

#### The unit vector in the direction of is:

Study Guide for Stewart's Multivariable Calculus, 8th

#### Find x.

Mathematics For Machine Technology 