3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { }...
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Transcript of 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { }...
![Page 1: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/1.jpg)
3-5 Working with Sets
![Page 2: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/2.jpg)
Different SetsRoster Set: lists the elements of a set within braces, { }
Example: the set of multiples of 2{2, 4, 6, 8, …}
Set-builder notation: describes the properties an element must have to be included in a set
Example: {2, 4, 6, 8, …} would be written as{x | x as a multiple of 2}read as: the set of all real numbers x, such that x is a multiple of 2
![Page 3: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/3.jpg)
Problem 1: Using Roster Form and Set-Builder Notation
How do you write “T is the set of natural numbers that are less than 6” in roster form and in set-builder notation?Roster Form:
Set-Builder Notation:
![Page 4: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/4.jpg)
How do you write “N is the set of even natural numbers that are less than or equal to 12” in roster form and in set-builder notation?Roster Form:
Set-Builder Notation:
![Page 5: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/5.jpg)
Problem 2: Inequalities and Set-Builder Notation
In set-builder notation, how do you write the solutions of
![Page 6: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/6.jpg)
In set-builder notation, how do you write the solutions of
![Page 7: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/7.jpg)
![Page 8: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/8.jpg)
A set A is a subset of set B if each element of A is also an element of B
Example: if and , then A is a subset of B
We can write this asA B
![Page 9: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/9.jpg)
Empty Set (null set): the set that contains no elements. The empty set is a subset of every set
Use { } or to represent the empty set
![Page 10: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/10.jpg)
Problem 3: Finding Subsets
What are all the subsets of {3, 4, 5}
![Page 11: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/11.jpg)
What are all the subsets of {a, b}
![Page 12: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/12.jpg)
Universal Set (Universe): the largest set you are using
Complement of a Set: the set of all elements in the universal set that are not in the set (you denote the complement of A by A’
![Page 13: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/13.jpg)
![Page 14: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/14.jpg)
Universal set U={months of the year} and set A ={months with exactly 31 days}. What is the complement of set A
![Page 15: 3-5 Working with Sets. Different Sets Roster Set: lists the elements of a set within braces, { } Example: the set of multiples of 2 {2, 4, 6, 8, …} Set-builder.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697bf701a28abf838c7d85b/html5/thumbnails/15.jpg)
Problem 4: Finding the Complement of a Set
Universal set U={king, queen, bishop, knight, rook, pawn} and set A is the set of chess pieces that move side to side. What is the complement of set A