Podcast
Questions and Answers
What is a set?
What is a set?
How is a set denoted?
How is a set denoted?
What is the roster form of a set?
What is the roster form of a set?
What is the set builder form of a set?
What is the set builder form of a set?
Signup and view all the answers
What is an empty set?
What is an empty set?
Signup and view all the answers
What is the union of two sets?
What is the union of two sets?
Signup and view all the answers
What is the intersection of two sets?
What is the intersection of two sets?
Signup and view all the answers
What is the complement of a set?
What is the complement of a set?
Signup and view all the answers
Study Notes
Sets
Definition of a Set
- A set is a collection of unique objects, known as elements or members, which can be anything (numbers, letters, objects, etc.)
- A set is denoted by a capital letter (e.g. A, B, C, etc.)
Representation of a Set
- There are two ways to represent a set:
- Roster Form: A set is represented by listing all its elements within curly braces {} Example: A = {1, 2, 3, 4, 5}
- Set Builder Form: A set is represented by describing the properties of its elements Example: A = {x: x is a natural number and x ≤ 5}
Types of Sets
- Empty Set (or Null Set): A set with no elements, denoted by ∅
- Singleton Set: A set with only one element
- Finite Set: A set with a finite number of elements
- Infinite Set: A set with an infinite number of elements
Operations on Sets
- Union of Sets: The union of two sets A and B, denoted by A ∪ B, is the set of all elements that are in A or in B or in both
- Intersection of Sets: The intersection of two sets A and B, denoted by A ∩ B, is the set of all elements that are common to both A and B
- Difference of Sets: The difference of two sets A and B, denoted by A - B, is the set of all elements that are in A but not in B
- Complement of a Set: The complement of a set A, denoted by A', is the set of all elements that are not in A
Sets
Definition of a Set
- A set is a collection of unique objects called elements or members
- Elements can be anything including numbers, letters, objects, etc.
Representation of a Set
- Sets can be represented in two ways: Roster Form and Set Builder Form
- Roster Form: lists all elements within curly braces {}
- Example of Roster Form: A = {1, 2, 3, 4, 5}
- Set Builder Form: describes properties of elements
- Example of Set Builder Form: A = {x: x is a natural number and x ≤ 5}
Types of Sets
- Empty Set (Null Set): has no elements, denoted by ∅
- Singleton Set: has only one element
- Finite Set: has a finite number of elements
- Infinite Set: has an infinite number of elements
Operations on Sets
- Union of Sets: A ∪ B is the set of all elements in A or B or both
- Intersection of Sets: A ∩ B is the set of all elements common to both A and B
- Difference of Sets: A - B is the set of all elements in A but not in B
- Complement of a Set: A' is the set of all elements not in A
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Learn about the definition and representation of sets, including roster form and set builder form. Understand the basics of set theory.