```

1. Introduction to Sets

2. Studying the concept of sets is inevitable to
learning algebra and other mathematical
concepts. In fact, we are always surrounded by
sets and its applications in our daily life.

3. At home, the most relevant
example of sets is in the kitchen.
Plates and bowls kept separate
from glasses, and utensil sets
are stored separately.

4. The application of sets in businesses is also
very useful in planning and operations.
Set is a vital part in categorizing or grouping
several items as well as comparing and
contrasting them.

5. In this lesson, you will learn the basic concept of sets including the subsets, universal sets, null
set, and cardinality of sets.

6. ● How do you represent a set?
● How do you write the subsets of a given set?

7. It is a collection of well-defined and distinct objects.
SET

8. •
SET

9. In this form, all elements of a set are listed and enclosed in
braces.
Elements are separated by a comma.
ROSTER FORM

10. •
ROSTER FORM

11. In this form, a common property of all the elements of a set is
written.
SET-BUILDER FORM

12. •
SET-BUILDER FORM

13. •
SUBSET

14. •
SUBSET

15. A set with no elements.
EMPTY SET OR A NULL SET

16. •
EMPTY SET OR A NULL SET

17. The set containing all objects or elements and of which all other
sets are subsets.

18. •

19. •
CARDINALITY OF A SET

20. •
CARDINALITY OF A SET

24. Example 2: Set 𝐴 consists of all positive multiples of 3 less
than 26 and set 𝐵 consists of all positive multiples of 8 less
than 89. Find |𝐴| and |𝐵|.

25. Example 2: Set 𝐴 consists of all positive multiples of 3 less
than 26 and set 𝐵 consists of all positive multiples of 8 less
than 89. Find |𝐴| and |𝐵|.

26. INDIVIDUAL PRACTICE:

27. GROUP PRACTICE: TO BE DONE BY 2 TO 5 GROUPS
Among six students in a class, namely, Jack, Karlo, Lexis,
Mario, Nathan, and Owen, only Jack, Lexis, and Mario love to
play basketball. Karlo, Nathan, and Owen, on the other hand,
love to play football. Define set 𝐴 as the set of students who
love to play basketball and set 𝐵 as the set of students who
love to play football. If the universal set contains all students
among them who love basketball or football, determine the
universal set.

28. ● A set is a collection of well-defined and distinct objects.
● A set is in roster form if all elements of a set are listed
and enclosed in braces. The elements are separated by a
comma.
● A set is in set-builder form when a common property of
all the elements of a set is written.

29. ● A set is said to be a subset of another set if all the
elements of it are contained in another set.
● Proper Subset is a subset which does not contain all the
same elements of a set.
● Empty or Null Set is a set with no elements.