SlideShare a Scribd company logo
Lets talk about
Definition:
A set is a collection of objects named elements.
Notation:
A set can be defined by listing its elements between
braces. Example: A = {1, 2, 3, 4, 5}.


If something is an element of a set we use .
If something is not an element we use .
Example: , .
A
89
A
2 

Lets talk about
If a set has no elements it is called the empty
set. It is written as ∅.
The universal set is the set of all elements
being considered. It is written 𝜉.
Lets talk about
The union of two sets, A and B, is the elements
in A or B or in both. It is written A ∪ B.

The intersection of two sets, A and B, is the
elements that are in A and B. It is written A ∩ B.
Example 1
A = {2, 3, 5, 7, 11, 13, 17, 19}
B = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
𝜉 is all the numbers 1 to 20.
a) Find A ∩ B
b) Find A ∪ B
c) What would a Venn diagram look like?
A B
A ∪ B
A B
A ∩ B
𝜉
𝜉
A B
A’
A B
A ∩ B’
𝜉
𝜉
Example 2
The Venn diagram shows the number of people
who like Pepsi Max and Coke Zero.
P C
a) Find P(P)
b) Find P(P ∪ C)
c) Find P(P ∩ C’)
31 5 2
9 𝜉
Example 3
A B
a) Find P(A) b) Find P(A’ ∩ B’)
c) Find P(A’ ∩ B)
d) Are A and B independent?
0.5 0.1 0.2
0.2 𝜉
If A and B are independent then the outcome of one
event doesn’t affect the probability of the other and
P(A) x P(B) = P(A ∩ B)
Example 4
P(A) = 0.25, P(B) = 0.6 and P(A ∩ B) = 0.05.
a) Draw a Venn diagram
b) Find P(A ∪ B)
c) Find P(A’ ∩ B)
d) Are A and B mutually exclusive?
If A and B are mutually exclusive then the events
cannot happen at the same time.
P(A ∩ B) = 0

More Related Content

Similar to Set-notation--venn-diagrams-and-probability [Read-Only].pptx

1. Real Numbers and Integer Exponent.pptx
1. Real Numbers and Integer Exponent.pptx1. Real Numbers and Integer Exponent.pptx
1. Real Numbers and Integer Exponent.pptx
mxian444
 
SET THEORY
SET THEORYSET THEORY
SET THEORY
shahzadebaujiti
 
Digital text sets pdf
Digital text sets  pdfDigital text sets  pdf
Digital text sets pdf
stephy1234
 
Mathematics Sets and Logic Week 1
Mathematics Sets and Logic Week 1Mathematics Sets and Logic Week 1
Mathematics Sets and Logic Week 1
Jasmine Jesse
 
Mtk3013 chapter 2-3
Mtk3013   chapter 2-3Mtk3013   chapter 2-3
Mtk3013 chapter 2-3
khairunnasirahmad
 
Set theory self study material
Set theory  self study materialSet theory  self study material
Set theory self study material
DrATAMILARASIMCA
 
Set theory and Venn Diagram.docx
Set theory and Venn Diagram.docxSet theory and Venn Diagram.docx
Set theory and Venn Diagram.docx
RenierXanderUy
 
Lecture 1 - Concept of Sets.pdf
Lecture 1 - Concept of Sets.pdfLecture 1 - Concept of Sets.pdf
Lecture 1 - Concept of Sets.pdf
SheinahdenMayTenerif
 
Ch1 sets and_logic(1)
Ch1 sets and_logic(1)Ch1 sets and_logic(1)
Ch1 sets and_logic(1)
Kwonpyo Ko
 
Chap2_SETS_PDF.pdf
Chap2_SETS_PDF.pdfChap2_SETS_PDF.pdf
Chap2_SETS_PDF.pdf
RatipornChomrit
 
Digital text book sets
Digital text book   setsDigital text book   sets
Digital text book sets
libinkalappila
 
2.1 Sets
2.1 Sets2.1 Sets
2.1 Sets
showslidedump
 
20200911-XI-Maths-Sets-2 of 2-Ppt.pdf
20200911-XI-Maths-Sets-2 of 2-Ppt.pdf20200911-XI-Maths-Sets-2 of 2-Ppt.pdf
20200911-XI-Maths-Sets-2 of 2-Ppt.pdf
MridulDhamija
 
Sets.ppt
Sets.pptSets.ppt
Sets.ppt
jaywarven1
 
Sets.ppt
Sets.pptSets.ppt
Sets.ppt
san_6384
 
Sets
SetsSets
Sets.ppt
Sets.pptSets.ppt
Sets.ppt
Sets.pptSets.ppt
Sets.ppt
IWa Suguitan
 
Sets.ppt
Sets.pptSets.ppt
Sets.ppt
ManilynSuarez2
 
Sets
SetsSets

Similar to Set-notation--venn-diagrams-and-probability [Read-Only].pptx (20)

1. Real Numbers and Integer Exponent.pptx
1. Real Numbers and Integer Exponent.pptx1. Real Numbers and Integer Exponent.pptx
1. Real Numbers and Integer Exponent.pptx
 
SET THEORY
SET THEORYSET THEORY
SET THEORY
 
Digital text sets pdf
Digital text sets  pdfDigital text sets  pdf
Digital text sets pdf
 
Mathematics Sets and Logic Week 1
Mathematics Sets and Logic Week 1Mathematics Sets and Logic Week 1
Mathematics Sets and Logic Week 1
 
Mtk3013 chapter 2-3
Mtk3013   chapter 2-3Mtk3013   chapter 2-3
Mtk3013 chapter 2-3
 
Set theory self study material
Set theory  self study materialSet theory  self study material
Set theory self study material
 
Set theory and Venn Diagram.docx
Set theory and Venn Diagram.docxSet theory and Venn Diagram.docx
Set theory and Venn Diagram.docx
 
Lecture 1 - Concept of Sets.pdf
Lecture 1 - Concept of Sets.pdfLecture 1 - Concept of Sets.pdf
Lecture 1 - Concept of Sets.pdf
 
Ch1 sets and_logic(1)
Ch1 sets and_logic(1)Ch1 sets and_logic(1)
Ch1 sets and_logic(1)
 
Chap2_SETS_PDF.pdf
Chap2_SETS_PDF.pdfChap2_SETS_PDF.pdf
Chap2_SETS_PDF.pdf
 
Digital text book sets
Digital text book   setsDigital text book   sets
Digital text book sets
 
2.1 Sets
2.1 Sets2.1 Sets
2.1 Sets
 
20200911-XI-Maths-Sets-2 of 2-Ppt.pdf
20200911-XI-Maths-Sets-2 of 2-Ppt.pdf20200911-XI-Maths-Sets-2 of 2-Ppt.pdf
20200911-XI-Maths-Sets-2 of 2-Ppt.pdf
 
Sets.ppt
Sets.pptSets.ppt
Sets.ppt
 
Sets.ppt
Sets.pptSets.ppt
Sets.ppt
 
Sets
SetsSets
Sets
 
Sets.ppt
Sets.pptSets.ppt
Sets.ppt
 
Sets.ppt
Sets.pptSets.ppt
Sets.ppt
 
Sets.ppt
Sets.pptSets.ppt
Sets.ppt
 
Sets
SetsSets
Sets
 

Recently uploaded

一比一原版(GWU,GW文凭证书)乔治·华盛顿大学毕业证如何办理
一比一原版(GWU,GW文凭证书)乔治·华盛顿大学毕业证如何办理一比一原版(GWU,GW文凭证书)乔治·华盛顿大学毕业证如何办理
一比一原版(GWU,GW文凭证书)乔治·华盛顿大学毕业证如何办理
bopyb
 
How To Control IO Usage using Resource Manager
How To Control IO Usage using Resource ManagerHow To Control IO Usage using Resource Manager
How To Control IO Usage using Resource Manager
Alireza Kamrani
 
一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理
一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理
一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理
hyfjgavov
 
一比一原版爱尔兰都柏林大学毕业证(本硕)ucd学位证书如何办理
一比一原版爱尔兰都柏林大学毕业证(本硕)ucd学位证书如何办理一比一原版爱尔兰都柏林大学毕业证(本硕)ucd学位证书如何办理
一比一原版爱尔兰都柏林大学毕业证(本硕)ucd学位证书如何办理
hqfek
 
一比一原版(UO毕业证)渥太华大学毕业证如何办理
一比一原版(UO毕业证)渥太华大学毕业证如何办理一比一原版(UO毕业证)渥太华大学毕业证如何办理
一比一原版(UO毕业证)渥太华大学毕业证如何办理
bmucuha
 
一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理
一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理
一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理
nyvan3
 
一比一原版(UCSF文凭证书)旧金山分校毕业证如何办理
一比一原版(UCSF文凭证书)旧金山分校毕业证如何办理一比一原版(UCSF文凭证书)旧金山分校毕业证如何办理
一比一原版(UCSF文凭证书)旧金山分校毕业证如何办理
nuttdpt
 
A presentation that explain the Power BI Licensing
A presentation that explain the Power BI LicensingA presentation that explain the Power BI Licensing
A presentation that explain the Power BI Licensing
AlessioFois2
 
一比一原版(曼大毕业证书)曼尼托巴大学毕业证如何办理
一比一原版(曼大毕业证书)曼尼托巴大学毕业证如何办理一比一原版(曼大毕业证书)曼尼托巴大学毕业证如何办理
一比一原版(曼大毕业证书)曼尼托巴大学毕业证如何办理
ytypuem
 
一比一原版英属哥伦比亚大学毕业证(UBC毕业证书)学历如何办理
一比一原版英属哥伦比亚大学毕业证(UBC毕业证书)学历如何办理一比一原版英属哥伦比亚大学毕业证(UBC毕业证书)学历如何办理
一比一原版英属哥伦比亚大学毕业证(UBC毕业证书)学历如何办理
z6osjkqvd
 
Open Source Contributions to Postgres: The Basics POSETTE 2024
Open Source Contributions to Postgres: The Basics POSETTE 2024Open Source Contributions to Postgres: The Basics POSETTE 2024
Open Source Contributions to Postgres: The Basics POSETTE 2024
ElizabethGarrettChri
 
06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM
06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM
06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM
Timothy Spann
 
一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理
一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理
一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理
aguty
 
DATA COMMS-NETWORKS YR2 lecture 08 NAT & CLOUD.docx
DATA COMMS-NETWORKS YR2 lecture 08 NAT & CLOUD.docxDATA COMMS-NETWORKS YR2 lecture 08 NAT & CLOUD.docx
DATA COMMS-NETWORKS YR2 lecture 08 NAT & CLOUD.docx
SaffaIbrahim1
 
一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理
一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理
一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理
1tyxnjpia
 
writing report business partner b1+ .pdf
writing report business partner b1+ .pdfwriting report business partner b1+ .pdf
writing report business partner b1+ .pdf
VyNguyen709676
 
一比一原版多伦多大学毕业证(UofT毕业证书)学历如何办理
一比一原版多伦多大学毕业证(UofT毕业证书)学历如何办理一比一原版多伦多大学毕业证(UofT毕业证书)学历如何办理
一比一原版多伦多大学毕业证(UofT毕业证书)学历如何办理
eoxhsaa
 
在线办理(英国UCA毕业证书)创意艺术大学毕业证在读证明一模一样
在线办理(英国UCA毕业证书)创意艺术大学毕业证在读证明一模一样在线办理(英国UCA毕业证书)创意艺术大学毕业证在读证明一模一样
在线办理(英国UCA毕业证书)创意艺术大学毕业证在读证明一模一样
v7oacc3l
 
原版一比一爱尔兰都柏林大学毕业证(UCD毕业证书)如何办理
原版一比一爱尔兰都柏林大学毕业证(UCD毕业证书)如何办理 原版一比一爱尔兰都柏林大学毕业证(UCD毕业证书)如何办理
原版一比一爱尔兰都柏林大学毕业证(UCD毕业证书)如何办理
tzu5xla
 
一比一原版(harvard毕业证书)哈佛大学毕业证如何办理
一比一原版(harvard毕业证书)哈佛大学毕业证如何办理一比一原版(harvard毕业证书)哈佛大学毕业证如何办理
一比一原版(harvard毕业证书)哈佛大学毕业证如何办理
taqyea
 

Recently uploaded (20)

一比一原版(GWU,GW文凭证书)乔治·华盛顿大学毕业证如何办理
一比一原版(GWU,GW文凭证书)乔治·华盛顿大学毕业证如何办理一比一原版(GWU,GW文凭证书)乔治·华盛顿大学毕业证如何办理
一比一原版(GWU,GW文凭证书)乔治·华盛顿大学毕业证如何办理
 
How To Control IO Usage using Resource Manager
How To Control IO Usage using Resource ManagerHow To Control IO Usage using Resource Manager
How To Control IO Usage using Resource Manager
 
一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理
一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理
一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理
 
一比一原版爱尔兰都柏林大学毕业证(本硕)ucd学位证书如何办理
一比一原版爱尔兰都柏林大学毕业证(本硕)ucd学位证书如何办理一比一原版爱尔兰都柏林大学毕业证(本硕)ucd学位证书如何办理
一比一原版爱尔兰都柏林大学毕业证(本硕)ucd学位证书如何办理
 
一比一原版(UO毕业证)渥太华大学毕业证如何办理
一比一原版(UO毕业证)渥太华大学毕业证如何办理一比一原版(UO毕业证)渥太华大学毕业证如何办理
一比一原版(UO毕业证)渥太华大学毕业证如何办理
 
一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理
一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理
一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理
 
一比一原版(UCSF文凭证书)旧金山分校毕业证如何办理
一比一原版(UCSF文凭证书)旧金山分校毕业证如何办理一比一原版(UCSF文凭证书)旧金山分校毕业证如何办理
一比一原版(UCSF文凭证书)旧金山分校毕业证如何办理
 
A presentation that explain the Power BI Licensing
A presentation that explain the Power BI LicensingA presentation that explain the Power BI Licensing
A presentation that explain the Power BI Licensing
 
一比一原版(曼大毕业证书)曼尼托巴大学毕业证如何办理
一比一原版(曼大毕业证书)曼尼托巴大学毕业证如何办理一比一原版(曼大毕业证书)曼尼托巴大学毕业证如何办理
一比一原版(曼大毕业证书)曼尼托巴大学毕业证如何办理
 
一比一原版英属哥伦比亚大学毕业证(UBC毕业证书)学历如何办理
一比一原版英属哥伦比亚大学毕业证(UBC毕业证书)学历如何办理一比一原版英属哥伦比亚大学毕业证(UBC毕业证书)学历如何办理
一比一原版英属哥伦比亚大学毕业证(UBC毕业证书)学历如何办理
 
Open Source Contributions to Postgres: The Basics POSETTE 2024
Open Source Contributions to Postgres: The Basics POSETTE 2024Open Source Contributions to Postgres: The Basics POSETTE 2024
Open Source Contributions to Postgres: The Basics POSETTE 2024
 
06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM
06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM
06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM
 
一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理
一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理
一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理
 
DATA COMMS-NETWORKS YR2 lecture 08 NAT & CLOUD.docx
DATA COMMS-NETWORKS YR2 lecture 08 NAT & CLOUD.docxDATA COMMS-NETWORKS YR2 lecture 08 NAT & CLOUD.docx
DATA COMMS-NETWORKS YR2 lecture 08 NAT & CLOUD.docx
 
一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理
一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理
一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理
 
writing report business partner b1+ .pdf
writing report business partner b1+ .pdfwriting report business partner b1+ .pdf
writing report business partner b1+ .pdf
 
一比一原版多伦多大学毕业证(UofT毕业证书)学历如何办理
一比一原版多伦多大学毕业证(UofT毕业证书)学历如何办理一比一原版多伦多大学毕业证(UofT毕业证书)学历如何办理
一比一原版多伦多大学毕业证(UofT毕业证书)学历如何办理
 
在线办理(英国UCA毕业证书)创意艺术大学毕业证在读证明一模一样
在线办理(英国UCA毕业证书)创意艺术大学毕业证在读证明一模一样在线办理(英国UCA毕业证书)创意艺术大学毕业证在读证明一模一样
在线办理(英国UCA毕业证书)创意艺术大学毕业证在读证明一模一样
 
原版一比一爱尔兰都柏林大学毕业证(UCD毕业证书)如何办理
原版一比一爱尔兰都柏林大学毕业证(UCD毕业证书)如何办理 原版一比一爱尔兰都柏林大学毕业证(UCD毕业证书)如何办理
原版一比一爱尔兰都柏林大学毕业证(UCD毕业证书)如何办理
 
一比一原版(harvard毕业证书)哈佛大学毕业证如何办理
一比一原版(harvard毕业证书)哈佛大学毕业证如何办理一比一原版(harvard毕业证书)哈佛大学毕业证如何办理
一比一原版(harvard毕业证书)哈佛大学毕业证如何办理
 

Set-notation--venn-diagrams-and-probability [Read-Only].pptx

  • 1. Lets talk about Definition: A set is a collection of objects named elements. Notation: A set can be defined by listing its elements between braces. Example: A = {1, 2, 3, 4, 5}.   If something is an element of a set we use . If something is not an element we use . Example: , . A 89 A 2  
  • 2. Lets talk about If a set has no elements it is called the empty set. It is written as ∅. The universal set is the set of all elements being considered. It is written 𝜉.
  • 3. Lets talk about The union of two sets, A and B, is the elements in A or B or in both. It is written A ∪ B.  The intersection of two sets, A and B, is the elements that are in A and B. It is written A ∩ B.
  • 4. Example 1 A = {2, 3, 5, 7, 11, 13, 17, 19} B = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} 𝜉 is all the numbers 1 to 20. a) Find A ∩ B b) Find A ∪ B c) What would a Venn diagram look like?
  • 5. A B A ∪ B A B A ∩ B 𝜉 𝜉
  • 6. A B A’ A B A ∩ B’ 𝜉 𝜉
  • 7. Example 2 The Venn diagram shows the number of people who like Pepsi Max and Coke Zero. P C a) Find P(P) b) Find P(P ∪ C) c) Find P(P ∩ C’) 31 5 2 9 𝜉
  • 8. Example 3 A B a) Find P(A) b) Find P(A’ ∩ B’) c) Find P(A’ ∩ B) d) Are A and B independent? 0.5 0.1 0.2 0.2 𝜉 If A and B are independent then the outcome of one event doesn’t affect the probability of the other and P(A) x P(B) = P(A ∩ B)
  • 9. Example 4 P(A) = 0.25, P(B) = 0.6 and P(A ∩ B) = 0.05. a) Draw a Venn diagram b) Find P(A ∪ B) c) Find P(A’ ∩ B) d) Are A and B mutually exclusive? If A and B are mutually exclusive then the events cannot happen at the same time. P(A ∩ B) = 0