![Page 1: Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should](https://reader035.vdocuments.mx/reader035/viewer/2022062518/5697bf761a28abf838c80bf3/html5/thumbnails/1.jpg)
Sets Part III
Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should get class notes from another student.
![Page 2: Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should](https://reader035.vdocuments.mx/reader035/viewer/2022062518/5697bf761a28abf838c80bf3/html5/thumbnails/2.jpg)
Example. Let U be the set of natural numbers less than or equal to 10.
Let A={2,4,6} and B={1,2,3,4,5}.
(Note: I constructed this Venn Diagram during class and referred to it throughout this presentation.)
Venn Diagrams
![Page 3: Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should](https://reader035.vdocuments.mx/reader035/viewer/2022062518/5697bf761a28abf838c80bf3/html5/thumbnails/3.jpg)
The complement of set A, symbolized by A′, is the set of all the elements in the universal set that are not in the set A.
A′ is read “A complement,” or “A prime.”
Definition of Set Complement
![Page 4: Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should](https://reader035.vdocuments.mx/reader035/viewer/2022062518/5697bf761a28abf838c80bf3/html5/thumbnails/4.jpg)
Example. Let U be the set of natural numbers less than or equal to 10.
Let A={2,4,6} and B={1,2,3,4,5}.
Find A′ and B′.
Set Complement
Answers:
A′ =
B′ =
![Page 5: Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should](https://reader035.vdocuments.mx/reader035/viewer/2022062518/5697bf761a28abf838c80bf3/html5/thumbnails/5.jpg)
The intersection of sets A and B, symbolized by A∩B, is the set containing all the elements that are common to both A and B.
A∩B is read “A intersect B,” or “A AND B.”
Definition of Set Intersection
![Page 6: Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should](https://reader035.vdocuments.mx/reader035/viewer/2022062518/5697bf761a28abf838c80bf3/html5/thumbnails/6.jpg)
Example. Let U be the set of natural numbers less than or equal to 10.
Let A={2,4,6} and B={1,2,3,4,5}.
Find A∩B.
Answer: A∩B =
Set Intersection
![Page 7: Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should](https://reader035.vdocuments.mx/reader035/viewer/2022062518/5697bf761a28abf838c80bf3/html5/thumbnails/7.jpg)
Let U = {a, b, c, d}A = {a, c} B = {b, d}
1. Find A′.
2. Find B′.
3. Find A′ ∩ B.
4. Find A∩B.
5. Find (A∩B)′.
Example
Answers:
![Page 8: Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should](https://reader035.vdocuments.mx/reader035/viewer/2022062518/5697bf761a28abf838c80bf3/html5/thumbnails/8.jpg)
The union of set A and set B, symbolized by A∪B, is the set containing all the elements that are members of set A or of set B (or of both sets).
A∪B is read “A union B,” or “A OR B.”
Definition of Set Union
![Page 9: Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should](https://reader035.vdocuments.mx/reader035/viewer/2022062518/5697bf761a28abf838c80bf3/html5/thumbnails/9.jpg)
Example. Let U be the set of natural numbers less than or equal to 10.
Let A={2,4,6} and B={1,2,3,4,5}.
Find A∪B.
Answer: A∪B =
Set Union
![Page 10: Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should](https://reader035.vdocuments.mx/reader035/viewer/2022062518/5697bf761a28abf838c80bf3/html5/thumbnails/10.jpg)
Let U = {a, b, c, d}A = {a, c} B = {b, d}
1. Find A∪B.
2. Find (A∪B )′.
3. Find A′ ∪ B.
4. Find (A′∩B)′.
Example
Answers:
![Page 11: Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should](https://reader035.vdocuments.mx/reader035/viewer/2022062518/5697bf761a28abf838c80bf3/html5/thumbnails/11.jpg)
The relationship between sets A, B, A∪B, and A∩B is given by the union rule:
n(A∪B) = n(A) + n(B) – n(A∩B)
Union Rule for Sets
Why? (We used a Venn Diagram to show this.)
![Page 12: Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should](https://reader035.vdocuments.mx/reader035/viewer/2022062518/5697bf761a28abf838c80bf3/html5/thumbnails/12.jpg)
1. If n(A) = 5, n(B) = 8, and n(A∩B) = 2, find n(A∪B).
Answer:
2. If n(A)=12, n(A∪B)=22, and n(A∩B)=10, find n(B).
Answer:
Two Possible Union Rule Test Problems:
![Page 13: Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you should](https://reader035.vdocuments.mx/reader035/viewer/2022062518/5697bf761a28abf838c80bf3/html5/thumbnails/13.jpg)
The difference of two sets A and B, symbolized A-B, is the set of elements that belong to set A but not to set B.
Example. Let U ={1,2,3,…,10}, A={2,4,6} and B={1,2,3,4,5}. Find A-B and B-A.
A-B=B-A=
Difference of Two Sets