MATHEMATICS 7 - WEEK 1

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