Here is the Venn diagram illustrating the universal set U and its subsets: 2 3 4 5 6 7 8 A B C J K Q H L F N The universal set U contains all the elements: {2,3,4,5,6,7,8,A,B,C,J,K,Q} Subset H = {J,Q,K} Subset L = {A,B,C} Subset F = {5,J} Subset N = {A,2,3,4} All the subsets are within the universal set based on their elements. The intersections of the subsets are also shown in the diagram.

1. Sherwin Roy C. Blason
Teacher III
Adelfa – 6:00 – 7:00 (Except Tuesday)
Sampaguita – 8:00 – 9:00 (Except Wednesday)
Gumamela – 10:20 – 11:20 (Except Tuesday)

2. Content Standards:
The learner demonstrates
understanding of key concepts of sets
and the real number system.
Performance Standards:
Welcome to class!

3. Learning Objectives

4. Establishing a
purpose for the
lesson
What comprises the set of aquatic animals that can swim?
What comprises the set of aquatic animals that have fins?
Is the set of aquatic animals that can swim a part of those that
have fins?
Is the set of aquatic animals with fins a part of those that
can swim?
What diagram was used to show the relationship between
the two sets?
Shrimp, Jellyfish, Sea Turtles, Whales, Fish, Sharks
Whales, Fish, Sharks
Only some animals that can swim are part of the group
that has fins.
Yes. Animals with fins can swim.
VENN DIAGRAM

5. Presenting examples /
instances of the lesson
The set of aquatic animals that can swim is the
universal set.
U is the set of aquatic animals that can swim.
The set of aquatic animals that have fins is the
subset of the universal set.

6. Presenting examples /
instances of the lesson Identify the elements of the universal set
What is the relationship of set B to set A?
U = { 1, 2, 3, 4, 5, 6}
U = A  B
Universal set is equal to the union of sets A and B
Since, all elements of set B can be found in set A.
Therefore, set B is a subset of set A.
B  A
What is the relationship of set A to set B?
Since, set A has more elements than set B.
Therefore, set A is a subset of set B.
A  B

7. Presenting examples /
instances of the lesson
What is the relation of set B to the universal Set U
Since, all elements of set B can be found in the Universal Set.
Therefore, set B is a subset of the universal set U.
B  U
B = {4, 5, 6}
U = {1, 2, 3, 4, 5, 6}
What is the relation of set A to the universal Set U
Since, all elements of set A can be found in the Universal Set.
Therefore, set A is a subset of the universal set U.
A  U
A = {1, 2, 3, 4, 5, 6}
U = {1, 2, 3, 4, 5, 6}

8. Let's
Solve
Together
Draw the Venn diagram of the given sets, and then identify the universal set and
the subsets
A = {all counting numbers less than 5}
A = {1, 2, 3, 4}
Verbal Description
A = { x | x are all counting numbers less than 5}
Set-Builder / Rule
Method
The set of All elements
of x
such that
Roster Method / Listing Method
B = {all odd numbers less than 10}
B = {1, 3, 5, 7, 9}
Verbal Description
B = { x | x are all odd numbers less than 10}
Set-Builder /
Rule Method
The set of All elements
of x
such that
Roster Method / Listing Method

9. Let's
Solve
Together
Draw the Venn diagram of the given sets, and then identify the universal set
and the subsets
A = {all counting numbers less than 5}
A = {1, 2, 3, 4}
Verbal Description
Roster Method / Listing Method
B = {all odd numbers less than 10}
B = {1, 3, 5, 7, 9}
Verbal Description
Roster Method / Listing Method
1
3
A B
U
2
4
5
7
9

10. Let's
Solve
Together
Draw the Venn diagram of the given sets, and then identify the universal set and t
subsets
1
3
A B
U
2
4
5
7
9
VENN DIAGRAM
1. Identify the elements of the Universal Set U. U = {1, 2, 3, 4, 5, 7, 9}
2. Identify the relationship of set A to the Universal Set.
A = {1, 2, 3, 4}
U = {1, 2, 3, 4, 5, 7, 9} A  U
3. Identify the relationship of set B to the Universal Set.
B = {1, 3, 5, 7, 9}
U = {1, 2, 3, 4, 5, 7, 9} B  U

11. Let's
Solve
Together
Draw the Venn diagram of the given sets, and then identify the universal set and t
subsets
1
3
A B
U
2
4
5
7
9
VENN DIAGRAM
4. Where can we find the elements 1 & 3?
We can find elements 1 & 3 at the intersection of set A and set B.
Therefore, the elements at the intersection of sets A and B are 1 & 3
(A  B) = {1, 3}
5. Identify the relationship of (A  B) to the universal set U.
(A  B ) = {1, 3}
U = {1, 2, 3, 4, 5, 7, 9} (A  B)  U

12. Application by Group
A = set of letters
B = set of vowels
Problem Number 1
U={1,2,3,4,5,6,7,8,9,10}
A = {2,4,6,8,10}
B = {1,2,3,4,5}
Problem Number 2

13. Making Generalizations
The universal set, or simply the universe, denoted by U, contains all the elements being
considered in a given situation.
What are Venn diagrams?
Pictorial representations of sets represented by closed figures are called set diagrams or Venn
diagrams. Venn diagrams are used to show relationships between sets and to illustrate various
operations like union, intersection, and difference.
We can express the relationship among sets through this in a more significant way. In this, A
rectangle is used to represent a universal set.
Circles or ovals are used to represent other subsets of the universal set.
This shows that every element of A is in the universal set.
If a set A is a subset of set B, then the circle representing set A is drawn inside the circle
representing set B.

14. Evaluation
Let U = {2,3,4,5,6,7,8,A,B,C,J,K,Q},
H = {J,Q,K},
L = {A,B,C},
F = {5,J}, and
N = {A,2,3,4}.
Illustrate the universal set and its subsets using the Venn diagram.