Pre-Algebra, Student Edition
Pre-Algebra, Student Edition
1st Edition
ISBN: 9780078885150
Author: McGraw-Hill
Publisher: Glencoe/McGraw-Hill
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Chapter 1.3, Problem 47HP

(a)

To determine

To Describe: Is the set of whole numbers closed under subtraction? If not give counterexample.

(a)

Expert Solution
Check Mark

Answer to Problem 47HP

No

Explanation of Solution

Given: If you take any two whole numbers and add them together the sum is always a whole number. This is a closure property for addition. The set of whole numbers is closed under addition.

No, set of whole numbers is not closed under subtraction

For example:

  5−8=−3

  −3 is not a whole number

(b)

To determine

To Describe: Suppose you had a very small set of numbers that contained only 0 and 1 . Would this set be closed under addition? If not give a counterexample.

(b)

Expert Solution
Check Mark

Answer to Problem 47HP

No

Explanation of Solution

Given: If you take any two whole numbers and add them together the sum is always a whole number. This is a closure property for addition. The set of whole numbers is closed under addition.

No, the set is not closed under addition

As

  1+1=2

Which is outside the set

(c)

To determine

To Describe:The closure property of multiplication using addition property.

(c)

Expert Solution
Check Mark

Answer to Problem 47HP

The property says that if you take any two whole numbers then the multiplication of both the numbers is always a whole number.

Explanation of Solution

Given: If you take any two whole numbers and add them together the sum is always a whole number. This is a closure property for addition. The set of whole numbers is closed under addition.

Closure property of multiplication

The property says that if you take any two whole numbers then the multiplication of both the numbers is always a whole number.

(d)

To determine

To Check:Is the set {0,1} is closed under multiplication? Explain.

(d)

Expert Solution
Check Mark

Answer to Problem 47HP

Yes

Explanation of Solution

Given: If you take any two whole numbers and add them together the sum is always a whole number. This is a closure property for addition. The set of whole numbers is closed under addition.

Yes,

The product of any two number in the range of {0,1} will remain in the set

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Chapter 1.3, Problem 46HP
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Chapter 1.3, Problem 48HP

Chapter 1 Solutions

Pre-Algebra, Student Edition

Ch. 1.1 - Prob. 1ACYPCh. 1.1 - Prob. 1BCYPCh. 1.1 - Prob. 2ACYPCh. 1.1 - Prob. 2BCYPCh. 1.1 - Prob. 2CCYPCh. 1.1 - Prob. 2DCYPCh. 1.1 - Prob. 3CYPCh. 1.1 - Prob. 1CYUCh. 1.1 - Prob. 2CYUCh. 1.1 - Prob. 3CYU
Ch. 1.1 - Prob. 4CYUCh. 1.1 - Prob. 5CYUCh. 1.1 - Prob. 6CYUCh. 1.1 - Prob. 7CYUCh. 1.1 - Prob. 8CYUCh. 1.1 - Prob. 9CYUCh. 1.1 - Prob. 10CYUCh. 1.1 - Prob. 11CYUCh. 1.1 - Prob. 12PPSCh. 1.1 - Prob. 13PPSCh. 1.1 - Prob. 14PPSCh. 1.1 - Prob. 15PPSCh. 1.1 - Prob. 16PPSCh. 1.1 - Prob. 17PPSCh. 1.1 - Prob. 18PPSCh. 1.1 - Prob. 19PPSCh. 1.1 - Prob. 20PPSCh. 1.1 - Prob. 21PPSCh. 1.1 - Prob. 22PPSCh. 1.1 - Prob. 23PPSCh. 1.1 - Prob. 24PPSCh. 1.1 - Prob. 25PPSCh. 1.1 - Prob. 26PPSCh. 1.1 - Prob. 27PPSCh. 1.1 - Prob. 28PPSCh. 1.1 - Prob. 29PPSCh. 1.1 - Prob. 30PPSCh. 1.1 - Prob. 31PPSCh. 1.1 - Prob. 32PPSCh. 1.1 - Prob. 33PPSCh. 1.1 - Prob. 34HPCh. 1.1 - Prob. 35HPCh. 1.1 - Prob. 36HPCh. 1.1 - Prob. 37HPCh. 1.1 - Prob. 38HPCh. 1.1 - Prob. 39STPCh. 1.1 - Prob. 40STPCh. 1.1 - Prob. 41STPCh. 1.1 - Prob. 42STPCh. 1.2 - Prob. 1ACYPCh. 1.2 - Prob. 1BCYPCh. 1.2 - Prob. 2ACYPCh. 1.2 - Prob. 2BCYPCh. 1.2 - Prob. 3ACYPCh. 1.2 - Prob. 3BCYPCh. 1.2 - Prob. 3CCYPCh. 1.2 - Prob. 4CYPCh. 1.2 - Prob. 1CYUCh. 1.2 - Prob. 2CYUCh. 1.2 - Prob. 3CYUCh. 1.2 - Prob. 4CYUCh. 1.2 - Prob. 5CYUCh. 1.2 - Prob. 6CYUCh. 1.2 - Prob. 7CYUCh. 1.2 - Prob. 8CYUCh. 1.2 - Prob. 9CYUCh. 1.2 - Prob. 10CYUCh. 1.2 - Prob. 11CYUCh. 1.2 - Prob. 12PPSCh. 1.2 - Prob. 13PPSCh. 1.2 - Prob. 14PPSCh. 1.2 - Prob. 15PPSCh. 1.2 - Prob. 16PPSCh. 1.2 - Prob. 17PPSCh. 1.2 - Prob. 18PPSCh. 1.2 - Prob. 19PPSCh. 1.2 - Prob. 20PPSCh. 1.2 - Prob. 21PPSCh. 1.2 - Prob. 22PPSCh. 1.2 - Prob. 23PPSCh. 1.2 - Prob. 24PPSCh. 1.2 - Prob. 25PPSCh. 1.2 - Prob. 26PPSCh. 1.2 - Prob. 27PPSCh. 1.2 - Prob. 28PPSCh. 1.2 - Prob. 29PPSCh. 1.2 - Prob. 30PPSCh. 1.2 - Prob. 31PPSCh. 1.2 - Prob. 32PPSCh. 1.2 - Prob. 33PPSCh. 1.2 - Prob. 34PPSCh. 1.2 - Prob. 35PPSCh. 1.2 - Prob. 36PPSCh. 1.2 - Prob. 37PPSCh. 1.2 - Prob. 38PPSCh. 1.2 - Prob. 39PPSCh. 1.2 - Prob. 40PPSCh. 1.2 - Prob. 41HPCh. 1.2 - Prob. 42HPCh. 1.2 - Prob. 43HPCh. 1.2 - Prob. 44HPCh. 1.2 - Prob. 45STPCh. 1.2 - Prob. 46STPCh. 1.2 - Prob. 47STPCh. 1.2 - Prob. 48STPCh. 1.2 - Prob. 49SRCh. 1.2 - Prob. 50SRCh. 1.2 - Prob. 51SRCh. 1.2 - Prob. 52SRCh. 1.2 - Prob. 53SRCh. 1.2 - Prob. 54SRCh. 1.2 - Prob. 55SRCh. 1.2 - Prob. 56SRCh. 1.2 - Prob. 57SRCh. 1.2 - Prob. 58SRCh. 1.2 - Prob. 59SRCh. 1.2 - Prob. 60SRCh. 1.2 - Prob. 61SCh. 1.2 - Prob. 62SCh. 1.2 - Prob. 63SCh. 1.2 - Prob. 64SCh. 1.3 - Prob. 1CYPCh. 1.3 - Prob. 2ACYPCh. 1.3 - Prob. 2BCYPCh. 1.3 - Prob. 2CCYPCh. 1.3 - Prob. 2DCYPCh. 1.3 - Prob. 3ACYPCh. 1.3 - Prob. 3BCYPCh. 1.3 - Prob. 4CYPCh. 1.3 - Prob. 1CYUCh. 1.3 - Prob. 2CYUCh. 1.3 - Prob. 3CYUCh. 1.3 - Prob. 4CYUCh. 1.3 - Prob. 5CYUCh. 1.3 - Prob. 6CYUCh. 1.3 - Prob. 7CYUCh. 1.3 - Prob. 8CYUCh. 1.3 - Prob. 9CYUCh. 1.3 - Prob. 10CYUCh. 1.3 - Prob. 11CYUCh. 1.3 - Prob. 12CYUCh. 1.3 - Prob. 13CYUCh. 1.3 - Prob. 14CYUCh. 1.3 - Prob. 15PPSCh. 1.3 - Prob. 16PPSCh. 1.3 - Prob. 17PPSCh. 1.3 - Prob. 18PPSCh. 1.3 - Prob. 19PPSCh. 1.3 - Prob. 20PPSCh. 1.3 - Prob. 21PPSCh. 1.3 - Prob. 22PPSCh. 1.3 - Prob. 23PPSCh. 1.3 - Prob. 24PPSCh. 1.3 - Prob. 25PPSCh. 1.3 - Prob. 26PPSCh. 1.3 - Prob. 27PPSCh. 1.3 - Prob. 28PPSCh. 1.3 - Prob. 29PPSCh. 1.3 - Prob. 30PPSCh. 1.3 - Prob. 31PPSCh. 1.3 - Prob. 32PPSCh. 1.3 - Prob. 33PPSCh. 1.3 - Prob. 34PPSCh. 1.3 - Prob. 35PPSCh. 1.3 - Prob. 36PPSCh. 1.3 - Prob. 37PPSCh. 1.3 - Prob. 38PPSCh. 1.3 - Prob. 39PPSCh. 1.3 - Prob. 40PPSCh. 1.3 - Prob. 41PPSCh. 1.3 - Prob. 42PPSCh. 1.3 - Prob. 43PPSCh. 1.3 - Prob. 44HPCh. 1.3 - Prob. 45HPCh. 1.3 - Prob. 46HPCh. 1.3 - Prob. 47HPCh. 1.3 - Prob. 48HPCh. 1.3 - Prob. 49STPCh. 1.3 - Prob. 50STPCh. 1.3 - Prob. 51STPCh. 1.3 - Prob. 52STPCh. 1.3 - Prob. 53SRCh. 1.3 - Prob. 54SRCh. 1.3 - Prob. 55SRCh. 1.3 - Prob. 56SRCh. 1.3 - Prob. 57SRCh. 1.3 - Prob. 58SRCh. 1.3 - Prob. 59SRCh. 1.3 - Prob. 60SRCh. 1.3 - Prob. 61SRCh. 1.3 - Prob. 62SRCh. 1.3 - Prob. 63SRCh. 1.3 - Prob. 64SCh. 1.3 - Prob. 65SCh. 1.3 - Prob. 66SCh. 1.3 - Prob. 67SCh. 1.3 - Prob. 68SCh. 1.3 - Prob. 69SCh. 1.3 - Prob. 70SCh. 1.3 - Prob. 71SCh. 1.4 - Prob. 1ACYPCh. 1.4 - Prob. 1BCYPCh. 1.4 - Prob. 1CCYPCh. 1.4 - Prob. 1DCYPCh. 1.4 - Prob. 2ACYPCh. 1.4 - Prob. 2BCYPCh. 1.4 - Prob. 3CYPCh. 1.4 - Prob. 4ACYPCh. 1.4 - Prob. 4BCYPCh. 1.4 - Prob. 1CYUCh. 1.4 - Prob. 2CYUCh. 1.4 - Prob. 3CYUCh. 1.4 - Prob. 4CYUCh. 1.4 - Prob. 5CYUCh. 1.4 - Prob. 6CYUCh. 1.4 - Prob. 7CYUCh. 1.4 - Prob. 8CYUCh. 1.4 - Prob. 9CYUCh. 1.4 - Prob. 10CYUCh. 1.4 - Prob. 11CYUCh. 1.4 - Prob. 12PPSCh. 1.4 - Prob. 13PPSCh. 1.4 - Prob. 14PPSCh. 1.4 - Prob. 15PPSCh. 1.4 - Prob. 16PPSCh. 1.4 - Prob. 17PPSCh. 1.4 - Prob. 18PPSCh. 1.4 - Prob. 19PPSCh. 1.4 - Prob. 20PPSCh. 1.4 - Prob. 21PPSCh. 1.4 - Prob. 22PPSCh. 1.4 - Prob. 23PPSCh. 1.4 - Prob. 24PPSCh. 1.4 - Prob. 25PPSCh. 1.4 - Prob. 26PPSCh. 1.4 - Prob. 27PPSCh. 1.4 - Prob. 28PPSCh. 1.4 - Prob. 29PPSCh. 1.4 - Prob. 30PPSCh. 1.4 - Prob. 31PPSCh. 1.4 - Prob. 32PPSCh. 1.4 - Prob. 33PPSCh. 1.4 - Prob. 34PPSCh. 1.4 - Prob. 35PPSCh. 1.4 - Prob. 36HPCh. 1.4 - Prob. 37HPCh. 1.4 - Prob. 38HPCh. 1.4 - Prob. 39HPCh. 1.4 - Prob. 40HPCh. 1.4 - Prob. 41STPCh. 1.4 - Prob. 42STPCh. 1.4 - Prob. 43STPCh. 1.4 - Prob. 44STPCh. 1.4 - Prob. 45SRCh. 1.4 - Prob. 46SRCh. 1.4 - Prob. 47SRCh. 1.4 - Prob. 48SRCh. 1.4 - Prob. 49SRCh. 1.4 - Prob. 50SRCh. 1.4 - Prob. 51SRCh. 1.4 - Prob. 52SCh. 1.4 - Prob. 53SCh. 1.4 - Prob. 54SCh. 1.4 - Prob. 55SCh. 1.4 - Prob. 56SCh. 1.4 - Prob. 57SCh. 1.5 - Prob. 1CYPCh. 1.5 - Prob. 2ACYPCh. 1.5 - Prob. 2BCYPCh. 1.5 - Prob. 1CYUCh. 1.5 - Prob. 2CYUCh. 1.5 - Prob. 3CYUCh. 1.5 - Prob. 4PPSCh. 1.5 - Prob. 5PPSCh. 1.5 - Prob. 6PPSCh. 1.5 - Prob. 7PPSCh. 1.5 - Prob. 8PPSCh. 1.5 - Prob. 9PPSCh. 1.5 - Prob. 10PPSCh. 1.5 - Prob. 11PPSCh. 1.5 - Prob. 12HPCh. 1.5 - Prob. 13HPCh. 1.5 - Prob. 14HPCh. 1.5 - Prob. 15STPCh. 1.5 - Prob. 16STPCh. 1.5 - Prob. 17STPCh. 1.5 - Prob. 18STPCh. 1.5 - Prob. 19SRCh. 1.5 - Prob. 20SRCh. 1.5 - Prob. 21SRCh. 1.5 - Prob. 22SRCh. 1.5 - Prob. 23SRCh. 1.5 - Prob. 24SRCh. 1.5 - Prob. 25SRCh. 1.5 - Prob. 26SRCh. 1.5 - Prob. 27SRCh. 1.5 - Prob. 28SRCh. 1.5 - Prob. 29SRCh. 1.5 - Prob. 30SRCh. 1.5 - Prob. 31SRCh. 1.5 - Prob. 32SCh. 1.5 - Prob. 33SCh. 1.5 - Prob. 34SCh. 1.5 - Prob. 35SCh. 1.6 - Prob. 1CYPCh. 1.6 - Prob. 2CYPCh. 1.6 - Prob. 3ACYPCh. 1.6 - Prob. 3BCYPCh. 1.6 - Prob. 3CCYPCh. 1.6 - Prob. 1CYUCh. 1.6 - Prob. 2PPSCh. 1.6 - Prob. 3PPSCh. 1.6 - Prob. 4PPSCh. 1.6 - Prob. 5PPSCh. 1.6 - Prob. 6PPSCh. 1.6 - Prob. 7PPSCh. 1.6 - Prob. 8PPSCh. 1.6 - Prob. 9PPSCh. 1.6 - Prob. 10PPSCh. 1.6 - Prob. 11PPSCh. 1.6 - Prob. 12PPSCh. 1.6 - Prob. 13PPSCh. 1.6 - Prob. 14PPSCh. 1.6 - Prob. 15PPSCh. 1.6 - Prob. 16HPCh. 1.6 - Prob. 17HPCh. 1.6 - Prob. 18HPCh. 1.6 - Prob. 19HPCh. 1.6 - Prob. 20HPCh. 1.6 - Prob. 21HPCh. 1.6 - Prob. 22HPCh. 1.6 - Prob. 23STPCh. 1.6 - Prob. 24STPCh. 1.6 - Prob. 25STPCh. 1.6 - Prob. 26STPCh. 1.6 - Prob. 27SRCh. 1.6 - Prob. 28SRCh. 1.6 - Prob. 29SRCh. 1.6 - Prob. 30SRCh. 1.6 - Prob. 31SRCh. 1.6 - Prob. 32SRCh. 1.6 - Prob. 33SRCh. 1.6 - Prob. 34SCh. 1.6 - Prob. 35SCh. 1.6 - Prob. 36SCh. 1.6 - Prob. 37SCh. 1.6 - Prob. 38SCh. 1.6 - Prob. 39SCh. 1 - Prob. 1QCCh. 1 - Prob. 2QCCh. 1 - Prob. 3QCCh. 1 - Prob. 4QCCh. 1 - Prob. 5QCCh. 1 - Prob. 6QCCh. 1 - Prob. 7QCCh. 1 - Prob. 8QCCh. 1 - Prob. 9QCCh. 1 - Prob. 10QCCh. 1 - Prob. 11QCCh. 1 - Prob. 12QCCh. 1 - Prob. 13QCCh. 1 - Prob. 14QCCh. 1 - Prob. 15QCCh. 1 - Prob. 16QCCh. 1 - Prob. 17QCCh. 1 - Prob. 18QCCh. 1 - Prob. 19QCCh. 1 - Prob. 1MCQCh. 1 - Prob. 2MCQCh. 1 - Prob. 3MCQCh. 1 - Prob. 4MCQCh. 1 - Prob. 5MCQCh. 1 - Prob. 6MCQCh. 1 - Prob. 7MCQCh. 1 - Prob. 8MCQCh. 1 - Prob. 9MCQCh. 1 - Prob. 10MCQCh. 1 - Prob. 11MCQCh. 1 - Prob. 12MCQCh. 1 - Prob. 13MCQCh. 1 - Prob. 14MCQCh. 1 - Prob. 15MCQCh. 1 - Prob. 16MCQCh. 1 - Prob. 17MCQCh. 1 - Prob. 18MCQCh. 1 - Prob. 19MCQCh. 1 - Prob. 20MCQCh. 1 - Prob. 21MCQCh. 1 - Prob. 22MCQCh. 1 - Prob. 23MCQCh. 1 - Prob. 24MCQCh. 1 - Prob. 25MCQCh. 1 - Prob. 1SGRCh. 1 - Prob. 2SGRCh. 1 - Prob. 3SGRCh. 1 - Prob. 4SGRCh. 1 - Prob. 5SGRCh. 1 - Prob. 6SGRCh. 1 - Prob. 7SGRCh. 1 - Prob. 8SGRCh. 1 - Prob. 9SGRCh. 1 - Prob. 10SGRCh. 1 - Prob. 11SGRCh. 1 - Prob. 12SGRCh. 1 - Prob. 13SGRCh. 1 - Prob. 14SGRCh. 1 - Prob. 15SGRCh. 1 - Prob. 16SGRCh. 1 - Prob. 17SGRCh. 1 - Prob. 18SGRCh. 1 - Prob. 19SGRCh. 1 - Prob. 20SGRCh. 1 - Prob. 21SGRCh. 1 - Prob. 22SGRCh. 1 - Prob. 23SGRCh. 1 - Prob. 24SGRCh. 1 - Prob. 25SGRCh. 1 - Prob. 26SGRCh. 1 - Prob. 27SGRCh. 1 - Prob. 28SGRCh. 1 - Prob. 29SGRCh. 1 - Prob. 30SGRCh. 1 - Prob. 1PTCh. 1 - Prob. 2PTCh. 1 - Prob. 3PTCh. 1 - Prob. 4PTCh. 1 - Prob. 5PTCh. 1 - Prob. 6PTCh. 1 - Prob. 7PTCh. 1 - Prob. 8PTCh. 1 - Prob. 9PTCh. 1 - Prob. 10PTCh. 1 - Prob. 11PTCh. 1 - Prob. 12PTCh. 1 - Prob. 13PTCh. 1 - Prob. 14PTCh. 1 - Prob. 15PTCh. 1 - Prob. 16PTCh. 1 - Prob. 17PTCh. 1 - Prob. 18PTCh. 1 - Prob. 19PTCh. 1 - Prob. 20PTCh. 1 - Prob. 21PTCh. 1 - Prob. 22PTCh. 1 - Prob. 23PTCh. 1 - Prob. 24PTCh. 1 - Prob. 25PTCh. 1 - Prob. 1ECh. 1 - Prob. 2ECh. 1 - Prob. 3ECh. 1 - Prob. 4ECh. 1 - Prob. 1STPCh. 1 - Prob. 2STPCh. 1 - Prob. 3STPCh. 1 - Prob. 4STPCh. 1 - Prob. 5STPCh. 1 - Prob. 6STPCh. 1 - Prob. 7STPCh. 1 - Prob. 8STPCh. 1 - Prob. 9STPCh. 1 - Prob. 10STPCh. 1 - Prob. 11STP

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