Chapter 2.1 Basic Set Concepts

Question 1

What are the three methods to represent sets?

Answer 1

Capital letters are generally used to name sets, Word descriptions, roster methods, and Roster Notation

Question 2

What are the examples of Word descriptions of the set?

Answer 2

P = {Washington, Adams, Jefferson, Madison, Monroe}
L = {a, b, c, d, e, f}
B is the set member of the Beatles in 1963.
S is the set of states whose names begin with the letter A

Question 3

What are the examples of the Roster Method?

Answer 3

C = {penny, nickel, dime, quarter, half-dollar}
B = { George Harrison, John Lennon, Paul McCartney, Ringo Starr}
S = {Alabama, Alaska, Arizona, Arkansas}

Question 4

What are the examples of the Set-Builder Notation?

Answer 4

A = {March, May}
B = {x|x was a member of the Beatles in 1963}
S = {x|x is a U.S. state whose name begins with the letter A}

Question 5

What are the two methods when using word description?

Answer 5

One method is a word description. We can describe set W as the set of the days of the week. A second mothod is the roster method. This involves listhe the elements of a set inside a pair of braces, { } the roster method also use only commas , are used to separate the elements of a set.

Question 6

What is a pair of braces, { } means?

Answer 6

The braces at the beginning and end indicate that we are representing a set.
Example: W = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

Question 7

Grouping sysmbols such as ____ and ____ are not used to represent sets.

Answer 7

parentheses ( ) and square brackets [ ]

Question 8

Example 1 of Representing a Set Using a Description.

Answer 8

P = {Washington, Adams, Jefferson, Madison, Monroe}
Solution: Set P is the set of the first five presidents of the United States.
Check Point 1: Write a word description of the set. L = {a, b, c, d, e, f}

Question 9

Example 2 Representing a Set Using the Roster Method.

Answer 9

Set C is the set of U.S. coins with a value of less than a dollar. Express this set using the roster method.
C = {penny, nickel, dime, quarter, haft-dollar}
Check Point 2: Set M is the set of months beginning with the letter A. Express this using the roster method. M = { } it means empthy set since there are no set of months beginneing with the letter A.

Question 10

Example 3 Converting from Set-Builder to Roster Notation.

Answer 10

Express set: A = {x|x is a month that begins with the letter M}
Solution: Set A is the set of all elements x such that x is a month beginning with the letter M. There are two such months, namely March and May. Thus,
A = {March, May}
Check Point 3: Express the set O = {x|x is a positive odd number less than 120} using the roster method.

Check Point 3: Express the set O = {x|x is a positive odd number less th

Question 11

How do you read this set-builder notation: W= {x|x is a day of whe week}

Answer 11

W: Set W
=: is
{: the set of
x: all elements x
|: such that
This is how you read it: Set W is the set of all elements x such that x is a day of the week.

Question 12

Do you have to use x to represent the variable in set-builder notation?

Answer 12

No. Any letter can be used to represent the variable. Thus {x|x is a day of the week}, {y|y is a day of the week}, and {z|z is a day of the week all represent the same set.

Question 13

How would you write the Word Description as an examples?

Answer 13

B is the set of members of the Beatles in 1963.
S is the set of states whose names begin with the letter A.

Question 14

How would you write the Roster Method?

Answer 14

B = {George Harrison, John Lennon, Paul McCartney, Ringo Starr}
S = {Alabama, Alaska, Arizona, Arkansas}

Question 15

How would you write the Set-Builder Notation?

Answer 15

B = {x|x was a member of the Beatles in 1963}
S = {x|x is a U.S. state whose name begins with the letter A}