
Concept explainers
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
(d) The set of integer powers of 2
(e) The set of ingredients in a peanut butter and jelly sandwich
a.

To write set in :-
(i)Roster Form
(ii)Set-Builder Form
Answer to Problem 1E
Roster Form :
Set-Builder Form : {
Explanation of Solution
Given :
The set of integers between 6 and 12 .
Clearly,
Hence, Roster Form :
Also, {
Hence, Set-Builder Form : {
b.

To write set in :-
(i)Roster Form
(ii)Set-Builder Form
Answer to Problem 1E
Roster Form :
Set-Builder Form : {
Explanation of Solution
Given :
The set of integers whose square is less than 17 .
Hence, Roster Form :
Also, {
c.

To write set in :-
(i)Roster Form
(ii)Set-Builder Form
Answer to Problem 1E
Roster Form :
Set-Builder Form : {
Explanation of Solution
Given :
The set of solutions to
Let,
Hence, Roster Form :
Also, {
d.

To write set in :-
(i)Roster Form
(ii)Set-Builder Form
Answer to Problem 1E
Roster Form :
Set-Builder Form : {
Explanation of Solution
Given :
The set of integer powers of 2 .
First of all, the set of integers is
Hence, the set of integral powers of 2 will be
Hence, Roster Form :
Also, Set-Builder Form : {
e.

To write set in :-
(i)Roster Form
(ii)Set-Builder Form
Answer to Problem 1E
Roster Form : { Bread, Peanut Butter, Jelly }
Set-Builder Form : {
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 : {
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Chapter I Solutions
A Transition to Advanced Mathematics
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