The document discusses sets and their properties. It defines sets as collections of objects and their elements. Finite sets can be counted, while infinite sets cannot. Two sets are equal if they contain the same elements, and equivalent if there is a one-to-one correspondence between elements. Sets can be defined using roster or set-builder notation.

1. SETS
well-defined sets,
universal sets, null
sets, cardinality of
sets
GRADE 7 – QUARTER 1 (WEEK 1)
7TH GRADE

2. OBJECTIVES:
1. Define Sets
2. Describe and Illustrate well-defined sets, null sets
and cardinality;
3. Determine the element/s of a given set
4. Identify the number of elements or its cardinality

3. UNLOCKING
WORDS!
INTEGERS – {…,-5, -4, -3, -2, -1, 0, 1,
2, 3, 4, 5,…}
WHOLE NUMBERS – {0, 1, 2, 3, 4,
5,…}
COUNTING/NATURAL NUMBERS –
{1, 2, 3, 4, 5,…}

4. UNLOCKING
WORDS!
EVEN NUMBERS – {2, 4, 6, 8,
10, 12,…}
ODD NUMBERS – {1, 3, 5, 7,
9,…}

5. WHAT IS SETS?
A set is a group or
collection of objects. It is
named using CAPITAL
letter. Each object in a set
is called a member or an
element of a set.

6. WHAT IS ELEMENTS?
∈ = an element
∉ = not an element

7. = {school days in a week}
A
= {Mon, Tues, Wed, Thur, Fri}
A
Mon, Tues, Wed, Thurs, Fri are called
elements of a given set.
Monday ∈ A Sunday ∉ A
Friday ∈ A Saturday ∉ A
EXAMPLES:

8. = {counting numbers less than 10}
B
= {1, 2, 3, 4, 5, 6, 7, 8, 9}
B
1, 2, 3, 4, 5, 6, 7, 8, 9 are called elements
of a given set.
2 ∈ B 100 ∉ B
8 ∈ B 27 ∉ B
EXAMPLES:

9. = {Primary colors}
C
= {red, blue, green, yellow}
C
Red, blue, green, yellow are called
elements of a given set.
red ∈ C violet ∉ C
blue ∈ C brown ∉ C
EXAMPLES:

10. = {even numbers}
A
= {odd numbers}
B
22 ___ A 46 ___ B
17 ___ B 45 ___ A
TRY THIS:
∈ ∉
∈ ∉

11. WELL-DEFINED SETS
A = {set of primary colors}
B = {set of handsome boys}
C = {set of excellent singers}
D = {set of toys}
E = {set of gadgets}
F = {set of popular actors}
NOT

12. EMPTY or NULL SETS
A set with no members or elements.
It is denoted by the symbol { } for
empty set and  for null set.
A = {set of a triangle with 4 sides}
B = {set of months in a year starts with
letter B}

13. CARDINALITY
Refers to the number of elements in
a given set. It is denoted by the
symbol n. “Cardinality of set A” is
written as n(A)

14. CARDINALITY
Examples:
A = {primary colors}
A = {red, blue, green, yellow}
n(A) = 4
B = {School days in a week}
B = {Mon, Tue, Wed, Thurs, Fri}
n(B) = 5

15. What if there is no elements in a given
set? What will be its cardinality?
A = {A square with 100 sides}
n(A) = { } n(A) = 0
n(A) = 

16. THE END
of part 1

17. CLASSIFICATION AND
WAYS OF NAMING A SET
02
Grade 7 – Quarter 1 (Week 1) (Part 2)

18. OBJECTIVES
1. Illustrate finite and infinite set;
2. Differentiate equal and equivalent sets;
3. Enumerate ways of naming a set

19. FINITE AND INFINITE SET
A set is finite if the number of elements in a
given set is a whole number {1, 2, 3,…,n},
otherwise it is said to be infinite.
1. FINITE SET – can be counted
2. INFINITE SET – cannot be counted

20. EXAMPLES:
A = {counting numbers}
A = {1, 2, 3, 4, 5,…}
Set A is an INFINITE SET
B = {counting numbers less than 7}
B = {1, 2, 3, 4, 5, 6}
Set B is an FINITE SET

21. EXAMPLES:
C = {letters in the English Alphabets}
C = {a, b, c, d, e,…,x, y, z}
Set C is an FINITE SET
D = {whole numbers greater than 9}
D = {10, 11, 12, 13, 14,…}
Set D is an INFINITE SET

22. Two sets are EQUAL if and only if
they contain exactly the same
elements
Two sets are EQUIVALENT if and
only if there is a one-to-one
correspondence between the sets.
EQUAL AND EQUIVALENT SETS

23. EXAMPLES:
A = {red, blue, yellow}
B = {red violet, blue}
C = {yellow, red, blue}
Set A and C are equal sets.
Set A and B are equivalent sets
Set B and C

24. EXAMPLES:
A = {1, 2, 3, 4, 5} C = {2, 3, 5, 4, 1}
B = {2, 3, 4, 6} D = {1, 3, 5, 7, 9}
Set C and Set D are…
Set A and Set C are…
Set B and Set C are…
Set A and Set D are…
EQUIVALENT SETS
EQUAL SETS
NEITHER
EQUIVALENT SETS

25. ROSTER METHOD
- Listing the elements
- If the set does not contain a very large
number of elements
SET-BUILDER NOTATION
- describing the elements
- if there are too many elements
WAYS OF DEFINING A SET

26. EXAMPLES
ROSTER METHOD:
A = {1, 2, 3, 4, 5}
B = {a, b, c, d, e}
SET-BUILDER NOTATION
C = {x|x is a letter in the alphabet}
read as “C is the set of all x such that
x is a letter in the alphabet”

27. ANOTHER EXAMPLES:
ROSTER METHOD SET-BUILDER NOTATION
A = {1, 2, 3, 4, 5} A = {x|x is a number less
than 6}
B = {2, 4, 6, 8, 10,…} B = {x|x is an even
number}
C = {a, e, i, o, u} C = {x|x is a vowel of the
alphabet

28. THE END
of part 2

29. EXERCISE

30. ________1. A = {1, 2, 3, 4, 5,…,25, 26, 27, 28}
________2. B = {…, -2, -1, 0, 1, 2, 3}
________3. C = {counting stars}
________4. A = { }
________5. D = {0.1, 0.2, 0.3, 0.4, 0.5,…}
________6. C = 
________7. B = {a, b, c, d, e, f}
________8. D = {set of 10 days in a week}
________9. A = {…, -3.1, -2.1, -1.1, -0.1, 1.1,…}
________10 D = {a, ab, abc, abcd, abcde}
Identify if the following set is FINITE SET,
INFINITE SET, and NULL/EMPTY SET

31. Identify the following sets if it is FINITE SET,
INFINITE SET and NULL/EMPTY SET.
______1. A = {10, 20, 30, 40, 50}
______2. B = {1, 2, 3,…}
______3. C = {2, 4, 6, 8, 10} and D= {1, 3, 5, 7, 9}
______4. A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
______5. B = { }

32. EQUAL SETS, EQUIVALENT SETS or NEITHER?
A = {all of English Alphabets} C = {E, A, C, D, B}
B = {J, K, L, M, N} D = {A, B, C, D, E}
1. Set A and Set D
2. Set B and Set C
3. Set A and Set A
4. Set B and Set D
5. Set C and Set D