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Sample Solution from

A Transition to Advanced Mathematics

8th Edition

ISBN: 9781285463261

Chapter I

Problem 1E

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Textbook Problem

Use these exercises to check your understanding. Answers appear at the end of the Answers to Selected Exercises.

1. Write each set in two ways: by listing its elements and by stating the property that determines membership in the set.(a) The set of integers between 6 and 12(b) The set of integers whose square is less than 17(c) The set of solutions to x 2 − 81 = 0
(d) The set of integer powers of 2
(e) The set of ingredients in a peanut butter and jelly sandwich

Expert Solution

To determine

To write set in :-

(i)Roster Form

(ii)Set-Builder Form

Answer

Roster Form : {7,8,9,10,11}

Set-Builder Form : { x : x is an integer between 6 and 12 }

Explanation of Solution

Given :

The set of integers between 6 and 12 .

Clearly, {7,8,9,10,11} is the set of integers lying between 6 and 12 .

Hence, Roster Form : {7,8,9,10,11}

Also, { x : x is an integer between 6 and 12 } is the set of all integers lying between 6 and 12 .

Hence, Set-Builder Form : { x : x is an integer between 6 and 12 }

Expert Solution

To determine

To write set in :-

(i)Roster Form

(ii)Set-Builder Form

Answer

Roster Form : {−4,−3,−2,−1,0,1,2,3,4}

Set-Builder Form : { x : x is an integer whose square is less than 17 }

Explanation of Solution

Given :

The set of integers whose square is less than 17 .

{−4,−3,−2,−1,0,1,2,3,4} is the set of all those integers whose squares are less than 17 .

Hence, Roster Form : {−4,−3,−2,−1,0,1,2,3,4}

Also, { x : x is an integer whose square is less than 17 } is the set-builder form for the given problem.

Expert Solution

To determine

To write set in :-

(i)Roster Form

(ii)Set-Builder Form

Answer

Roster Form : {−9,9}

Set-Builder Form : { x : x is the solution of x2−81=0 }

Explanation of Solution

Given :

The set of solutions to x2−81=0

Let,

x2−81=0

⇒x2=81⇒x=81⇒x=±9 (Square root both sides)

Hence, Roster Form : {−9,9}

Also, { x : x is the solution of x2−81=0 } is the set-builder form .

Expert Solution

To determine

To write set in :-

(i)Roster Form

(ii)Set-Builder Form

Answer

Roster Form : {....,14,12,1,2,4,....}

Set-Builder Form : { x : x is an integral power of 2 }

Explanation of Solution

Given :

The set of integer powers of 2 .

First of all, the set of integers is Z={....,−2,−1,0,1,2,....}

Hence, the set of integral powers of 2 will be {....,2−2,2−1,20,21,22,....}

Hence, Roster Form : {....,2−2,2−1,20,21,22,....} = {....,14,12,1,2,4,....}

Also, Set-Builder Form : { x : x is an integral power of 2 }

Expert Solution

To determine

To write set in :-

(i)Roster Form

(ii)Set-Builder Form

Answer

Roster Form : { Bread, Peanut Butter, Jelly }

Set-Builder Form : { x : x is an ingredient in peanut butter and jelly sandwich }

Explanation of Solution

Given :

The set of ingredients in a peanut butter and jelly sandwich .

This delicious sandwich is made up of bread, peanut butter and jelly .

Hence, Roster Form : { Bread, Peanut Butter, Jelly }

Also, Set-Builder Form : { x : x is an ingredient in peanut butter and jelly sandwich }

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