KS4 Grade 9 - SET LANGUAGE & NOTATION
Lesson 4...APPLICATIONS OF VENN DIAGRAMS
![Picture](/uploads/1/3/3/4/13343229/1185822.png?349)
Eg. The Venn Diagram of the left represents 16 students where 12 study Art, 8 study Music and 1 studies neither.
a) Write down the value of s
s = 1
b) Find value of q
p + q + r + s = 16 --> p + q + r = 15
If p + q = 12 --> p = 12 - q and q + r = 8 --> r = 8 - q
Then 12 - q + q + 8 - q = 15 --> 20 - q = 15 --> q = 20 - 15
Therefore q = 5
c) Write down value of p and r
p = 7, r = 3
TASK 1 - Textbook Pg22 Ex1.3
HOMEWORK - Venn Diagram HWMK WS
a) Write down the value of s
s = 1
b) Find value of q
p + q + r + s = 16 --> p + q + r = 15
If p + q = 12 --> p = 12 - q and q + r = 8 --> r = 8 - q
Then 12 - q + q + 8 - q = 15 --> 20 - q = 15 --> q = 20 - 15
Therefore q = 5
c) Write down value of p and r
p = 7, r = 3
TASK 1 - Textbook Pg22 Ex1.3
HOMEWORK - Venn Diagram HWMK WS
![](http://www.weebly.com/weebly/images/file_icons/pdf.png)
venn_diag_final_hw.pdf | |
File Size: | 407 kb |
File Type: |
Lesson 3...VENN DIAGRAMS
![Picture](/uploads/1/3/3/4/13343229/1340631.jpg?255)
A VENN DIAGRAM is a pictorial representation of the relationship between two or more sets
Note: If ε is a universal set and A is any set, then
n(A) + n(A') = n(ε)
The INTERSECTION of two or more sets is the set which contains the elements common to both, or all, of the original sets such that
A ∩ B = {x : x ∈ A and x ∈ B}
The UNION of two or more sets includes all of the elements in both, or all, of the original sets such that
A U B = {x : x ∈ A or x ∈ B}
TASK 1 - Textbook Pg17 Ex1.2 All Qs
HOMEWORK - None set
Note: If ε is a universal set and A is any set, then
n(A) + n(A') = n(ε)
The INTERSECTION of two or more sets is the set which contains the elements common to both, or all, of the original sets such that
A ∩ B = {x : x ∈ A and x ∈ B}
The UNION of two or more sets includes all of the elements in both, or all, of the original sets such that
A U B = {x : x ∈ A or x ∈ B}
TASK 1 - Textbook Pg17 Ex1.2 All Qs
HOMEWORK - None set
Lesson 2...SET THEORY
![Picture](/uploads/1/3/3/4/13343229/5115513.jpg?193)
EQUAL SETS - if two or more sets contain exactly the same elements
SUBSET - if the elements of one set A can be contained within another set B, then A is a SUBSET of B [A ⊆ B], or a PROPER SUBSET [A ⊂ B] if n(A) < n(B)
A UNIVERSAL SET is a set which consists of all elements under consideration
If ε is the universal set, the COMPLEMENT of P is the set
P' = {x : x ∉ P, x ∈ ε}
TASK 1 - Pg7 Ex1.1B Odd Qs
HOMEWORK - None set
SUBSET - if the elements of one set A can be contained within another set B, then A is a SUBSET of B [A ⊆ B], or a PROPER SUBSET [A ⊂ B] if n(A) < n(B)
A UNIVERSAL SET is a set which consists of all elements under consideration
If ε is the universal set, the COMPLEMENT of P is the set
P' = {x : x ∉ P, x ∈ ε}
TASK 1 - Pg7 Ex1.1B Odd Qs
HOMEWORK - None set
Lesson 1...INTRO TO SETS
![Picture](/uploads/1/3/3/4/13343229/6934683.jpg?213)
A SET is a collection of well-defined elements (objects)
Eg. Take the word MATHEMATICS...
M = {a,c,e,h,i,m,s,t}
a ∈ M a 'belongs to' M
b ∉ M a 'is not a member of' M
A FINITE SET has a limited number of values
An INFINITE SET has an unlimited number of values
Eg. The positive integers less than 12 is a Finite Set
A = {1,2,3,...,11} '...' denotes 'other missing elements'
n(A) = 11 n(A) denotes 'number of elements in set A'
Using Set-builder Notation for the example above A = {x : x is a positive integer and x < 12} or A = {x : x ∈ Z, x < 12}
HOMEWORK - Read examples on Pg3-4 [inc. 'Empty Set' and 'Dummy Variable'] and attempt Pg4 Ex 1.1A Q1-4,6
Eg. Take the word MATHEMATICS...
M = {a,c,e,h,i,m,s,t}
a ∈ M a 'belongs to' M
b ∉ M a 'is not a member of' M
A FINITE SET has a limited number of values
An INFINITE SET has an unlimited number of values
Eg. The positive integers less than 12 is a Finite Set
A = {1,2,3,...,11} '...' denotes 'other missing elements'
n(A) = 11 n(A) denotes 'number of elements in set A'
Using Set-builder Notation for the example above A = {x : x is a positive integer and x < 12} or A = {x : x ∈ Z, x < 12}
HOMEWORK - Read examples on Pg3-4 [inc. 'Empty Set' and 'Dummy Variable'] and attempt Pg4 Ex 1.1A Q1-4,6