Mathematics 7
Basic Set
Operations and
Venn Diagram
Week 2
Review: (From our Previous Lesson)
Direction: Arrange the Following scrabble words. Write all your answers on the answer sheet provided
on this module.
1. It is a well – defined collection of distinct objects.
E T S ________________________
2. It is the set of all possible elements of any set.
L U A N S I R V E E T S ___________________
3. A set with no element.
U L N L E T S ____________________
4. Two sets that contain the same number of elements.
T E N Q L U A I V E T S E _________________________
5. It is a diagram that makes use of geometric shapes to show relationships between sets.
N N V E M D A I A G R _______________________
6. These are sets with a defined number of elements.
E F T I I N _______________________
7. This is a method describing a set by listing each element of the set inside the symbol { }.
R R O E T S _______________________
8. Two sets that contain the same elements.
L E A Q U T S E ______________________
9. These are sets having no element in common.
T D N I I O S J __________________________
10. It is a method of describing a set in words.
L V A E B R ________________________
What I Need To Know:
Notations and Symbols
- Symbols
- Meaning
- Example
- How to read the symbols
Basic Set Operations
Venn Diagram
What I Know:
(Activity)
Direction: Answer the following given activity below to test yourself what you already know or what
activity you don’t know. Write your answers on the answer sheet provided on this module.
1. What Diagram is used for sets relationship?
A. Floiw Chart C. Orgazitional Chart
B. Graphic Diagram D. Venn Diagram
2. This means that it belongs to a given set or member of a set, what is it?
A. Equivalent C. Proper
B. Elements D. Subset
3. Which of the following is the symbol of “Not a Proper Subset”?
A. ϵ C. ⊄
B. ∅ D. ≈
4. Which of the following is the symbol of a “Null set”?
A. ϵ C. ⊄
B. ∅ D. ≈
5. This is a set that the elements belong to both A and B?
A. Cardinality Set C. Intersection Set
B. Equivalent Set D. Null Set
What’s New: 1
Today let’s learn together about The Basic Set Operations and Venn Diagram.
What Is It:
Notations and Symbols
Notations and Symbols
Symbols
Symbols Meaning
Meaning Example
Example HowTo
How toRead
Read
⊆
∈ ElementSubset { 9,14,28
If A = {5,1.10, } ⊆ {then
15, 20} 9,14,28 } 5 ∈AA⊆ B
Every element in A is also 2. If A = { 2, 4, 6, 8, …}
an element
Element in B. 5 ∈ A, 10
means that and∈ BA,=15{ 1,∈ 2, 204,∈5, …“5
A, 3, A element
is an is a subset
of A”
A⊆B of B.
it belongs to a given A. }, then A ⊆ B.
set or member of a
⊈ set. Not a Subset If A = { 2, 4, 6, 8 } and A⊈B
Set A does not belong to B = { 1, 3, 5, 7 }, then A is not
⊈ B.15, 20} then a∉A
a subset
∉ NotSet
an B.
element If A = {5,A 10,
A⊈ B “a is not
of B.
∉ A, and 7 ∉ A. an element of A”
Cardinality of A A = {a, e, i, o, u}, n(A) = 5
n(A)
⊂ Proper Subset A = {a, b, c} and A ⊂B
“The cardinality
The number of of set A is 5.”
Set A Bcontains
= {a, b,5c, d},
elements
Thereinis the set one
at least Set A is a proper
elements.
n(A)
A ⊂B element in B not = 5. element in A is
Each subset
includedSets
Equivalent A = {1, 2, 3,also an element in B.
4}, and toAset
≈ BB.
≈ in A. B = {m, a, t, h} is at least one
There
Two sets that Both setselement
contain in B not
four Set A is equivalent to
contain the same elements. contained in A and set B.
number that element is “d”.
⊄ Not a Proper Subset
of elements. C = {1, 2, 3 } and D C ⊄D
Equal Sets = { 1, 2,
C = {a, e, i, o, u} and3} C=D
= The elements in C D are i, All elements in D are Set C is not
= {e, o, u, a}
C ⊄D Two equal to the elements
sets that Sets C and alsoD elements
contain thein C. Set Ca is
proper
equalsubset
to set
in D.
contain the same same elements. D. to set B.
elements.
Notations and Symbols
Symbols Meaning Example How to Read
∅ or { } Empty set or Null set Set M is an empty set or null
A set with no M={ } set.
element
U Universal Set Universal Set
The set of all
U
possible elements
of any set.
Venn Diagram
Meaning Representation Explanation
2
These are diagrams that All elements
make use of geometric in A and B
shapes to show relationships are
between sets. contained in
the
universal
set.
Sets A and
B are
disjoint
sets.
Union and Intersection of Sets
In arithmetic, we have Four Basic Operations such as addition, subtraction, multiplication, and
division of numbers. In sets, we have also the Four Basic Set Operation. In this lesson, we will only
discuss the first two operations namely: Union and Intersection of Sets. The last two operations will be
discussed in the next lesson.
Basic Set Operations
3
Symbol Meaning Venn Diagram Examples
∪ Union of Sets 1. Find the union of A =
{ 2, 3, 4} and
The set of B = { 3, 4, 5}.
elements that
A∪B Solution:
belongs to set A
A ∪ B = { 2, 3, 4, 5 }
or set B or both.
List all the elements
read as
in set A and all of the
A ∪ B is shaded elements in set B. If
A union B
an element is in both
sets, we list it only
once.
Reminder!
To make it uniform if the
elements of the given set
are numbers, then arrange
your final answer in
increasing order.
Basic Set Operations
Symbol Meaning Venn Diagram Examples
∩ Intersection of 1. Find the intersection of
A = { 2, 3, 4} and
Sets
B = { 3, 4, 5}.
A∩B
Solution:
The set of
A ∩ B = { 3, 4 }
elements
belongs to both The common
elements of Sets
A and B.
read as A and B are 3
Set of the A ∩ B is shaded
and 4.
An
intersection common
B
elements in A
2. Given:
and B. A = {1, 2, 3, 4, 5, 6}, B =
{2, 4, 6}, and
C = {1, 3, 5, …}
Find: a. A ∩ C
b. B ∩ C
Solution:
a. A ∩ C = {1, 3, 5}
A ∩ B ∩C is shaded b. B ∩ C = { } or ∅
No common element in
sets B and C.
4
More Examples
Given: X = {2, 4, 6, 8, 10, 12}, Y = {3, 6, 9, 12, 15}
and Z = {1, 4, 7, 10, 13, 16}.
Find:
1. X ∪ Y 3. X ∪ Z ∩ Y
2. Y ∩ Z 4. (Y ∩ X) ∪ Z
Solution:
1. X ∪ Y = {2, 4, 6, 8, 10, 12 } ∪ { 3, 6, 9, 12, 15 }
X ∪ Y
First, list the given elements
of Sets X and Y.
X ∪ Y = {2, 3, 4, 6, 8, 9, 10, 12, 15} Finally, get the union of X and Y.
This means that combine the
elements. If an element is in both
sets, we list it only once.
2. Y ∩ Z = {3, 6, 9, 12, 15} ∩ {1, 4, 7, 10, 13, 16}
Y ∩ Z
First, list the given elements
of Sets Y and Z.
Y∩Z={}
Finally, get the intersection of Y
and Z. Note that the intersection is
the "common element". Since
there is no common element, so
the answer is a null or empty set.
3. X ∪ Z ∩ Y = {2, 4, 6, 8, 10, 12} ∪ {1, 4, 7, 10, 13, 16} ∩ {3, 6, 9, 12, 15}
X ∪ Z ∩ Y
First, list the given elements of
sets X, Z, and Y.
X∪Z∩Y = {1, 2, 4, 6, 7, 8, 10, 12, 13, 16}∩ {3, 6, 9, 12, 15}
Second, solve the union of sets
X and Z. Here is the answer to
X ∪ Z.
X∪Z∩Y = { 6, 12 } 5
Finally, solve the intersection of
X ∪ Z and Y. Then, here is the
final answer.
4. ( Y ∩ X ) ∪ Z = ({ 3, 6, 9, 12, 15 } ∩ { 2, 4, 6, 8, 10, 12 } ) ∪ { 1, 4, 7, 10, 13, 16 }
( Y ∩ X ) ∪ Z
First, list the given elements of
sets Y, X, and Z.
( Y ∩ X ) ∪ Z = { 6, 12 } ∪ { 1, 4, 7, 10, 13, 16 }
Second, solve the operation
inside the parenthesis which is
the intersection of Y and X.
Here is the answer.
( Y ∩ X ) ∪ Z = { 1, 4, 6, 7, 10, 12, 13, 16 }
Finally, get the union of the
sets ( Y ∩ X ) and Z. Then,
here is the final answer.
Complement and Difference of Sets
In the previous lesson, we have learned the union and intersection of sets. Now, we will discuss
two more Set Operations which are the Complement of a set and Difference of two sets.
Basic Set Operations
Symbol Meaning Venn Diagram Examples
A’ or Ac A complement Given:
of a Set U = {1, 2, 3, 4, 5} and
Set of all A = {1, 3, 5}. Find A’.
elements in the Solution:
universal set U
read as that are not in A’ = {2, 4}
A complement set A.
The
A’ is shaded complement
of A is the set
of elements
in U but not
in A. These
elements are 2
and 4.
Basic Set Operations
6
Symbol Meaning Venn Diagram Examples
A–B Difference of Given:
Sets A = {3, 4, 5, 6} and
The set B = {2, 4, 6, 8}
containing
elements Find:
read as of set A but not a. A – B
A minus B in B.
All elements of b. B – A
A except the Solution:
elements of B.
a. A – B = {3, 5 }
A – B is shaded
b. B – A= {2, 8}
More Examples
Given: U = {1, 2, 3, 4, 5}
A = {1, 3, 5}
B = {3, 4, 5} and
C = {2, 4}
Find: a.) A’ ∪ B’
b.) (A∩ C)’
c.) B – C’
Solution:
a.) A’ ∪ B’ = {1, 3, 5}’ ∪ {3, 4, 5}’
A ’ ∪ B ’
First, list the elements of sets A and B.
A’ ∪ B’ = {2, 4} ∪ { 1,7 2}
Second, solve
A’ and B’. Here
is the result.
A’ ∪ B’ = {1, 2, 4}
Finally, get the
union of A’ and
B’. Here is the
final answer.
b.) (A ∩ C )’ = ( {1, 3, 5} ∩ { 2, 4} )’
( A ∩ C )’
First, list the elements
of sets A and C.
(A ∩ C)’ = ({ } )’ Second, solve the operation inside
the parenthesis which is the
intersection of A and C. Here is
the answer.
(A ∩ C)’ = {1 ,2, 3, 4, 5}
Finally, get the complement. Note
that the complement of an empty
set is the universal set.
c.) B – C’ = {3, 4, 5} – { 2 , 4 }’
B – C ‘
First, list the
elements of Sets
B and C.
B – C’ = {3, 4, 5} – { 1, 3, 5 }
Second, solve the
complement of C.
Here is the result.
B – C’ = {4}
Finally, solve the
difference
between B
and C. Here is the
What’s More (Activities)
ACTIVITIES
Test Yourself!
Direction: Answers all your activities and write your answers on the Answer Sheet provided on this
module
Activity I:
Find Me! (Find the words written below, you can use different colors you want)
Y M K A T J B K C B L D K Z O
O H A L E V R P X L I I P S P
J D N O S G M X E P T L S X L
W G B Y P S T K G Y B Z K C X
U L Z L M E J J D I O X E J F
H O Y E Q A R J Y M K Q L V V
N E Z L V Z P A R E E S E M K
P B V N O I N U T P W E M D A
M N S J Y K I T E I O I E L H
B X N X Q D O T C T O C N P Y
I N T E R S E C T I O N T U I
H Y Y P V R M I U M H F S R G
N X O Z S T F P M C X A S L H
X D K V A T S O P Z L C L Z G
R W G V U C N B F S K K S U P
COMMON ELEMENTS INTERSECTION SET
OPERATION VENN UNION
Activity II:
To solve numbers 1 – 5, use the given Venn Diagram below. (write your answer in the space provided.)
1. A ∩ B 3. A ∩ B’ 5. (A ∩ B )’
2. A’ 4. (A ∪ B)’
9
Activity III: (Multiple Choice)
1. What is the symbol used for intersection?
A. ∪ B. ∩ C. ⊆ D. ∈
2. What is the complement of ∅ ?
A. { } C. U
B. {1} D. {0}
3. What is the complement of {3, 4}, if U = {1, 2, 3, 4}?
A. { } C. { 1 }
B. { 0 } D. { 1, 2 }
4. What is A ∪ B, if A= {0, 2, 3, 4, 9, 11} and B = {2, 3, 6, 8, 9, 10}?
A. {0, 4 11} C. {6, 8, 9, 10, 11}
B. {2, 3, 6, 9} D. {0, 2, 3, 4, 6, 8, 9, 10, 11 }
5. If P = {a, b, c, d, e}, Q = {a, c, e, d, t } and R = { t, d, c, b, e }, then
what is P∩ Q ∩ R?
A. {a, c} C. {c, d}
B. {a, c, e} D. { c, d, e }
6. Given U = {a, d, c, r, f, v, t, w}, H= { a, d, c, v } and J = { r, c, f },
what is H ∩ J’?
A. {c } C. { a, d, v, t }
B. {a, d, v} D. {a, d, r, f, v, t }
Activity IV:
1. Which of the following represents the shaded area in the Venn Diagram
below?
A. B’ C. B – A
B. A D. A – B
2. What does the shaded region below represent?
A. (A ∪ B) ∩ C C. A U (B – C)
B. A ∩ B ∩ C D. A’ ∪ B ∩ C
10
Answer Sheet in Mathematics 7 (Week 2)
Name:____________________________________________________________
Review:
1. 6.
2. 7.
3. 8.
4. 9.
5. 10.
What I Know:
1. 2. 3. 4. 5.
ACTIVITIES:
Activity 1
Y M K A T J B K C B L D K Z O
O H A L E V R P X L I I P S P
J D N O S G M X E P T L S X L
W G B Y P S T K G Y B Z K C X
U L Z L M E J J D I O X E J F
H O Y E Q A R J Y M K Q L V V
N E Z L V Z P A R E E S E M K
P B V N O I N U T P W E M D A
M N S J Y K I T E I O I E L H
B X N X Q D O T C T O C N P Y
I N T E R S E C T I O N T U I
H Y Y P V R M I U M H F S R G
N X O Z S T F P M C X A S L H
X D K V A T S O P Z L C L Z G
R W G V U C N B F S K K S U P
Activity II
1. A ∩ B 3. A ∩ B’ 5. (A ∩ B )’
2. A’ 4. (A ∪ B)’
Activity III
1. 3. 5
2. 4. 6.
Activity IV
1. 2.
