Math 7 | Lesson 2 Set Operations and the Venn Diagram

Set Operations and the Venn Diagram
Lesson 2
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Objectives
At the end of this lesson, you should be able to:
• perform set operations like union, intersection,
complement and difference; and
• use a Venn diagram to illustrate set operations
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Learn about it!
• A Venn diagram is used to represent relationships
between a collection of objects or sets.
• As shown below, a Venn diagram usually has a
rectangle with circles inside. The rectangle represents
the universal set and the circles inside represent the
different subsets in the universal set. The letter name
of the set is written beside it.
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Venn Diagram
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• In the illustration, the universal set contains natural
numbers from 1 to 10, or
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
• Set A = 1, 3, 5, 7, 9}
• Set B = { 6, 7, 8, 9, 10}
• Notice that 2 and 4 are outside the circles that
represent sets A and B. This means that both
numbers are **not** elements of either A or B.
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• There are four basic set operations that are best
understood using Venn diagrams. These are union
intersection, complementand difference.
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Set Operations
• Given two sets A and B:
• Union (∪) – A ∪ B is the set that contains all the
elements in either A or B.
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Set Operation
Intersection (∩) – A ∩ 𝐵 is the set that contains all
common elements between sets A and B.
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Set Operation
Complement (‘)
A’ is the set that contains all elements in the universal set
that are not in set A.
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Set Operation
Difference (-) – A - B is the set that contains all elements
of A that are not in B.
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Example
• Consider the Venn diagram from the previous chapter.
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Find A ∪ B
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A ∪ B = {1, 3, 5, 6, 7, 8, 9, 10}

Find A ∩ B
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A ∩ B = {7, 9}

Find A’
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A’ = {2, 4, 6, 8, 10}

Find A - B
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A’ = {1, 3, 5}

Try it!
Illustrate the given sets A and B using a Venn diagram
and perform the following operations:
A = {1, 2, 3}
B = {-6, -4, -2}
1. A ∪ B
2. A ∩ B
3. B’
4. A - B
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Try it Solution
A = {1, 2, 3} and B = {-6, -4, -2} can be illustrated as:
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Try it Solution
1. A ∪ B = {-6, -4, -2, 1, 2, 3}
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Try it Solution
2. A ∩ B = {} or ∅
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Try it Solution
2. B’ = {1, 2, 3}
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Try it Solution
2. A - B = {1, 2, 3}
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Tips
• Venn diagrams are especially helpful when
dealing with three or more sets.
• The elements of a set are unique. When one
element is repeated, there is no need to rewrite
the element in the set.
• Example: {[% 5, 7, 9, 2, 5, 7, 5 %]} [% = %] {[%
5, 7, 9, 2 %]}
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Keypoints
• A Venn diagram is used to represent relationships
between a collection of objects or sets.
• Given two sets A and B, there are four basic set
operations that can be performed:
•
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Keypoints
• Union - A ∪ B is the set that contains all the
elements in either A or B.
• Intersection - A ∩ B is the set that contains all
common elements between sets A and B.
• Complement - A’ is the set that contains all elements
in the universal set that are not in set A.
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Keypoints
• Difference - A − B is the set that contains all the
elements of A that are not in B.
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Question 1
What do you call the illustration used to represent the
relationships between sets?
• Select your answer.
a) Circle graph
b) Venn diagram
c) Pie chart
d) Circle diagram
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Question 2
Which of the following represents the intersection of
two sets?
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Question 3
Which of the following is the symbol for set
complement?
a) ∩
b) ∪
c) –
d) ‘
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Question 4
Given the following Venn diagram, what is A ∪ B
Select your answer.
a) {9, 10, 11}
b) {2, 4, 6}
c) {6}
d) {1, 2, 3, 4, 5, 6}
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Question 5
Given the following Venn diagram, what is B – A?
Select your answer.
a) {1, 3, 5, 6}
b) {2, 4, 9, 10, 11}
c) {2, 4}
d) {1, 2, 3, 4, 5, 6}
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Question 6
Given the following Venn diagram, what is B’?
Select your answer.
a) {1, 3, 5, 9, 10, 11}
b) {9, 10, 11}
c) {1, 3, 5, 6, 9, 10, 11}
d) {1, 3, 5, 6}
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Question 7
The students of a Grade 7 class were grouped under
sets S, T and V. What is V ∩ T
a) {Drew, Jade, Glen}
b) {Blair, Erin, Francis, Ira}
c) {Case, Drew}.
d) {Drew, Jade}
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Question 8
If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∪ B?
Select your answer.
a) {1, 2, 3, 3, 5, 5, 7, 7, 9}
b) {1, 2, 3, 5, 7, 9}
c) {2, 3, 5, 7, 9}
d) {2, 3, 5, 7}
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Question 9
If P is the set of whole numbers less than 6, Q is the set of
even numbers greater than 3 but less than 9, and R is the
set of positive factors of 6, then what is (P ∩ Q) ∪ R?
a) {1, 2, 3, 4, 6}
b) {0, 1, 2, 3, 4, 5}
c) {4, 6, 8}
d) {4, 5, 6}
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Question 10
Using the Venn diagram above, what is the set (S ∩ T) ∪ V?
Select your answer.
a) {Alex, Glen, Hunter, Jade}
b) {Casey, Drew, Glen, Jade}
c) {Casey, Drew, Glen}
d) {Alex, Casey, Drew, Hunter}
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Math 7 | Lesson 2 Set Operations and the Venn Diagram

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