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INTRODUCTION TO SETS

GRADE 7 MATHEMATICS QUARTER I

Objectives:

define set;
describe and illustrate well-defined sets and null sets;
determine the element/s of a given set; and
identify the number of elements or its cardinality.

UNLOCKING WORDS DIFFICULTY

INTEGERS

{-∞ , 0, +∞ }

WHOLE NUMBERS

{0, 1, 2, 3, 4, 5, 6, ... }

COUNTING/NATURAL NUMBERS

{1, 2, 3, 4, 5, 6,...}

EVEN NUMBERS

{2, 4, 6, ,8, 10,...}

ODD NUMBERS

{1, 3, 5, 7, 9,...}

PRIME NUMBERS

{2, 3, 5, 7, 11,...}

COMPOSITE NUMBERS

{4, 6, 8, 9, 10,...}

PERFECT SQUARES

{1, 4, 9, 16, 25,...}

MULTIPLES

{skip counting by...}

FACTORS

{Numbers which can be divided without remainder}

SET

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.

INFINITE SET

∈ - the symbol used for element

∉ - the symbol used for not an element

SET

A = {shoe, jacket, cap}

A = {set of objects that can be worn}

B = {ball, doll, toy car}

B = {set of toys}

C = {orange, mango, banana}

C = {set of fruits}

EXAMPLE:

EXAMPLE 1: School days in a week

A = {school days in a week}

A = { Mon, Tue, Wed, Thurs, Fri}

Monday ∈ A (Monday is an element of set A)
Tuesday ∈ A (Tuesday is an element of set A)
Wednesday ∈ A (Wednesday is an element of set A)
Thursday ∈ A (Thursday is an element of set A)
Friday ∈ A (Friday is an element of set A)
Saturday (Saturday is NOT an element of set A)
Sunday (Sunday is NOT an element of set A)

Mon, Tues, Wed, Thurs, Fri, are called members or elements of a given set.

EXAMPLE 2: Counting numbers less than 5

B = {counting number less than 5}

B = { 1, 2, 3, 4}

1, 2, 3, 4 are called members or elements of a given set.

EXAMPLE 3: Primary Colors

C = {primary colors}

C = { yellow, red, blue}

yellow, red, blue are called members or elements of a given set.

EXAMPLE 4: Even, odd, and counting numbers

A = {even numbers}

B = { odd numbers}

C = {counting numbers}

Fill in the blank with ∈ or ∉

2 A
8 B
7 C
3 B
-2 C
5 A

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WELL-DEFINED SET

In mathematics, set is a well-defined group or collection of objects that share common characteristics. The objects contained in the set are called elements.
A set can be named using capital letters like A, B, C, D,…Z and we use braces { } to group the elements of set separated by commas.
If a set contains many elements, we often use three dots, …, called ellipsis.

*Note: In listing the elements of the set, each distinct element is listed once and the order of the element does not matter.

EXAMPLE OF WELL-DEFINED SETS:

The set of primary colors

M = {𝑟𝑒𝑑, 𝑦𝑒𝑙𝑙𝑜𝑤, 𝑏𝑙𝑢𝑒}

The set of all multiples of 5.

Y = {5, 10, 15, …}

The set of all even numbers.

E = { 2, 4, 6,…}

The set of letter in the word “arrange”.

O = { 𝑎, 𝑟, 𝑛, 𝑔, 𝑒}

EXAMPLE OF NOT WELL-DEFINED SETS:

The set of famous dancers.
The set of punctual students in your class.
The set of honest people

*Note: The sets given above are not well-defined since people will have different point of views on famous dancers, punctual students and honest people.

ACTIVITY: IDENTIFY THE SETS IF WELL-DEFINED OR NOT

Identify whether each of the following sets is well-defined or not

The set of young politicians.
The set of types of matter.
The set of versatile actress.
The set of all oceans of the earth.
The set of months containing 31 days.
The set of tasty food.
The set of planets in our solar system.
The set of durable bags.
The set of consonants in the English Alphabet
The set of even counting numbers.

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EMPTY OR NULL SET

A set with no member or element is an empty set or null set. It s denoted by symbol for empty set is { } and ∅ for null set.

EXAMPLE OF EMPTY OR NULL SETS:

A = {set of triangle with four sides}

B = {set of months in a year star with B}

C = {set of whole numbers less than 0}

D = {set of months with 35 days }

E = {set of cars with 60 doors.}

CARDINALITY OF SETS

Refers to the number of elements in a given set. It is denoted by the symbol "n". Cardinality of Set is written as n(A).

EXAMPLE OF CARDINALITY OF SETS:

The cardinal number of set A, denoted by n(A), is the number of elements in set A.

Thus, in A = {1,3,5, 7}, n(A) = 4 because set A contains 4 elements.

Examples: Find the cardinality of the following sets.

Set D is the set of vowels in English alphabet.

Solution: D = {𝑎, 𝑒,𝑖, 𝑜, 𝑢}

Answer: n(D) = 5

Set R is the set of letters in the word “difficulty”.

Solution: R = {𝑑, 𝑖, 𝑓, 𝑐, 𝑢, 𝑙,𝑡, 𝑦}

Answer: n(R) = 8

Set M is the set of odd numbers between 1 and 3.

Solution: M = { } or M = ∅

Answer: n(M) = 0

Set E is the set of letters in the word “survivor”.

Solution: E = {𝑠, 𝑢, 𝑟, 𝑣, 𝑖, }

Answer: n(E) = 6

Set K is the set of counting numbers less than 5.

Solution: K = {1, 2, 3, 4}

Answer: n(K) = 4

ACTIVITY: FIND THE CARDINALITY

Find the cardinality of the following sets.

Set A is the set of days in a week.
Set B is the set of letters in the word “recognition”.
Set C is the set of even numbers less than 2.
Set D is the set of odd numbers between 3 and 9.
Set E is the set of factors of 12.

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VIDEO LESSON FOR BETTER UNDERSTANDING:

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