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Questions and Answers
The set {California, Colorado, Connecticut} is expressed using ________
the roster method
The set {x|x is a U.S.state whose name begins with the letter C} is expressed using ______
set builder notation
A set that contains no elements is called the ______ and is represented by ______
empty/null set; ⌀ or { }
The symbol ∈ is used to indicate that an object ________ of a set
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The set of {1,2,3,4,5...} is called the set of ____________.
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Two sets that contain the same number of elements are called ______
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Two sets that contain the same number of elements are called ______
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The collection of current NFL players is not well defined and therefore is not a set.
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Write a description of the set {Aquarius, Aries}:
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Write a description of the set {16, 17, 18, 19,...}:
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Give a word description for the set {15,16,17,18,...,29}:
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Express the given set using the roster method: The set of natural numbers less than 3.
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Express the given set using the roster method: The set of natural numbers less than or equal to 10.
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Express the set using the roster method: The set of odd natural numbers less than 5.
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Express the set using the roster method: {x | x∈N and x≤8}.
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Express the set using the roster method: {x | x∈N and 6≤x≤9}.
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Determine if the set is the empty set: {x | x is a living British monarch born before 1800}.
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Determine if the set is the empty set: {x | x8}.
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Determine if the set is the empty set: {x | x∈N and 10}.
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Study Notes
Set Theory Concepts
- Roster method is used to explicitly list all elements of a set, e.g., {California, Colorado, Connecticut}.
- Set builder notation defines a set by a property shared by its members, e.g., {x|x is a U.S. state whose name begins with the letter C}.
Types of Sets
- The empty or null set contains no elements represented by ⌀ or {}.
- An element of a set is denoted by the symbol ∈, indicating membership.
Number Sets
- Natural numbers are represented by the set {1, 2, 3, 4, 5...} and include all positive integers.
Set Equivalence and Equality
- Equivalent sets contain the same number of elements but may differ in their members.
- Equal sets contain precisely the same members.
Well-defined Collections
- A collection is well-defined if it can be distinctly specified, e.g., the collection of current NFL players qualifies as a set.
Descriptions of Sets
- Sets can be described using various methods, such as naming or criteria:
- Example: {Aquarius, Aries} can be described as "the set of Zodiac signs that begin with A".
- Example: {16, 17, 18, 19,...} is described as "all natural numbers greater than 15".
Using Roster Method
- The roster method allows for easy visualization, e.g.,
- Natural numbers less than 3: {1, 2}.
- Natural numbers less than or equal to 10: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Specific Set Expressions
- Odd natural numbers less than 5 are expressed as {1, 3}.
- For x ∈ N and x ≤ 8, the set is {1, 2, 3, 4, 5, 6, 7, 8}.
- For x ∈ N and 6 ≤ x ≤ 9, the set is {6, 7, 8, 9}.
Empty Sets
- Certain conditions lead to the empty set, for example:
- Living British monarchs born before 1800 result in an empty set.
- The set of all x that satisfy x < 0 for all natural numbers is also an empty set.
Studying That Suits You
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Description
Test your knowledge of set theory concepts with these flashcards from Math 1100 Chapter 2.1. You'll learn about roster methods, set builder notation, and the empty set. Perfect for mastering the basics of sets and their representations.
