INTRODUCTION TO SETS || GRADE 7 MATHEMATICS Q1

Summary

This video script covers various mathematical concepts about sets, including definitions, examples, and classifications. It explains well-defined and not well-defined sets, empty sets, and the cardinality of sets. The video uses practical examples to illustrate different types of numbers, such as integers, whole numbers, counting numbers, even and odd numbers, prime and composite numbers, perfect squares, multiples, and factors. Additionally, it provides visual aids to group objects by their characteristics. The explanation aims to help viewers understand and differentiate between these fundamental mathematical concepts.

Takeaways

• 📚 Introduction to sets and their various concepts, including well-defined and not well-defined sets.
• 🔢 Explanation of different types of numbers such as integers, whole numbers, counting numbers, even numbers, odd numbers, prime numbers, composite numbers, and perfect squares.
• ✖️ Multiples and factors are discussed with examples, highlighting how numbers can be divided without remainders.
• 📋 Grouping objects into sets based on their characteristics, such as clothing items, toys, and fruits.
• 🔠 Sets are named using capital letters, and each object in a set is called a member or an element.
• 🔄 Symbols used to denote elements and non-elements in a set, with examples of well-defined and not well-defined sets.
• 🌌 Empty sets (null sets) are explained, including how to denote them and examples like triangles with four sides and months starting with 'B'.
• 🔢 Cardinality refers to the number of elements in a given set, denoted by 'n'. Examples of calculating cardinality are provided.
• ❌ Cardinality of empty sets is always zero, as they contain no elements.
• 📽️ The video concludes with a reminder to like, subscribe, and click the bell button for more content.

Q & A

What is a well-defined set?

A well-defined set is a collection of distinct objects that can be clearly determined whether an object belongs to it or not. For example, the set of primary colors (red, blue, yellow) is well-defined because we can clearly identify which colors are primary.

Why is 'set of beautiful girls in school' not a well-defined set?

The 'set of beautiful girls in school' is not a well-defined set because the term 'beautiful' is subjective and can vary from person to person. Therefore, it cannot be clearly determined whether a girl belongs to this set.

What is an empty set or null set?

An empty set or null set is a set that contains no elements. For example, the set of triangles with four sides is an empty set because no triangles have four sides.

What is cardinality?

Cardinality refers to the number of elements in a given set. It is denoted by a small letter 'n' followed by the name of the set enclosed in parentheses. For example, if set A is the set of primary colors, its cardinality is 3, as it contains three elements: red, blue, and yellow.

What are integers?

Integers are numbers that include all positive whole numbers, negative whole numbers, and zero. They can be written as ..., -3, -2, -1, 0, 1, 2, 3, ...

What are whole numbers?

Whole numbers are non-negative numbers starting from zero. They include 0, 1, 2, 3, and so on up to positive infinity.

What are counting or natural numbers?

Counting or natural numbers are positive integers starting from 1 and increasing to positive infinity. They include 1, 2, 3, 4, and so on.

What are prime numbers?

Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. Examples include 2, 3, 5, 7, 11, 13, 17, 19, etc.

What are composite numbers?

Composite numbers are numbers that have more than two divisors. They can be divided by 1, themselves, and at least one other number. Examples include 4, 6, 8, 9, 12, etc.

What are perfect squares?

Perfect squares are numbers that can be expressed as the product of an integer multiplied by itself. Examples include 1 (1x1), 4 (2x2), 9 (3x3), 16 (4x4), 25 (5x5), and so on.

Outlines

00:00

🎓 Introduction to Sets

The paragraph introduces the concept of sets in mathematics, discussing different types of sets such as well-defined and not well-defined sets, null or empty sets, and elements of sets. It emphasizes the importance of understanding these fundamental concepts for further discussions.

05:03

🔢 Types of Numbers in Sets

This paragraph covers various types of numbers used in sets, including integers, whole numbers, counting numbers, even numbers, odd numbers, prime numbers, and composite numbers. It explains each type with examples and highlights their significance in the context of sets.

10:03

🗂 Examples of Sets and Classification

The focus here is on grouping objects into sets based on their characteristics. Examples include grouping shoes, jackets, and cups as wearable items, and balls, dolls, and toy cars as toys. The paragraph also covers the concept of categorizing fruits and toys into well-defined sets.

15:04

📝 Elements and Membership in Sets

This section explains how sets are named and how elements are identified within sets. It covers the use of capital letters for set names and the concept of elements or members of a set, providing examples of school days, primary colors, and counting numbers.

20:05

🧩 Well-Defined and Not Well-Defined Sets

The paragraph distinguishes between well-defined and not well-defined sets, using examples like primary colors (well-defined) and beautiful girls (not well-defined). It highlights the importance of clear definitions in determining set membership.

25:05

🔍 Null Sets and Cardinality

This part discusses null or empty sets, which have no elements, and the concept of cardinality, which refers to the number of elements in a set. It provides examples of null sets and explains how to determine the cardinality of both null and non-null sets.

✅ Summary and Conclusion

The final paragraph summarizes the key points covered in the video, reiterating the importance of understanding sets, elements, and types of numbers. It encourages viewers to like, subscribe, and click the bell button for more content.

Keywords

💡Set

A set is a collection of distinct objects, considered as an object in its own right. For example, in the video, a set is defined as a group of objects with the same characteristics, like the set of school days or the set of primary colors.

💡Element

An element is an individual object within a set. The video explains that elements are the members of a set, such as 'Monday' being an element of the set of school days.

💡Well-defined set

A well-defined set is a set where it is clear whether an object belongs to it. The video provides examples like the set of primary colors (well-defined) and the set of beautiful girls in school (not well-defined).

💡Empty set

An empty set, or null set, is a set with no elements. The video gives examples such as the set of triangles with four sides, which is an empty set because no triangles have four sides.

💡Cardinality

Cardinality refers to the number of elements in a set. The video explains that the cardinality of a set is the count of its elements, such as the cardinality of the set of school days being five.

💡Prime numbers

Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. The video lists examples like 2, 3, 5, and 7 as prime numbers.

💡Composite numbers

Composite numbers are natural numbers that have more than two positive divisors. The video gives examples such as 4, 6, 8, and 9, which are composite because they can be divided by numbers other than 1 and themselves.

💡Even numbers

Even numbers are integers divisible by 2 without a remainder. The video mentions examples like 2, 4, 6, and 8, which are all even numbers.

💡Odd numbers

Odd numbers are integers not divisible by 2. The video lists examples like 1, 3, 5, and 7 as odd numbers.

💡Perfect squares

Perfect squares are numbers that are the square of an integer. The video provides examples like 1, 4, 9, and 16, which are perfect squares because they can be expressed as 1x1, 2x2, 3x3, and 4x4, respectively.

Highlights

Introduction to the concept of sets in mathematics, including well-defined sets and null sets.

Explanation of different types of numbers: integers, whole numbers, counting numbers, even numbers, odd numbers, prime numbers, and composite numbers.

Definition and examples of even and odd numbers, emphasizing skip counting and multiples.

Prime numbers are described as numbers that have only two factors: 1 and themselves.

Composite numbers are numbers that have more than two factors, with examples provided.

Discussion of why the number one is neither prime nor composite.

Explanation of perfect squares and how they are obtained by multiplying a number by itself.

Illustration of multiples and how they relate to skip counting.

Factors are defined as numbers that divide another number without leaving a remainder.

Grouping objects into sets based on common characteristics, with examples provided.

Explanation of elements of a set and how to denote them using symbols.

Definition of well-defined and not well-defined sets, with examples illustrating the difference.

Introduction to the concept of empty sets or null sets and their notation.

Cardinality is defined as the number of elements in a given set, with examples to illustrate.

Demonstration of how to determine the cardinality of sets, including sets with no elements.

Transcripts

[Music]

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discuss um intro about sets OD total

Honiton and Lahontan concepts about sets

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video natal una edit Malala Manhattan

and inaba and said Pamela why is he not

in human examples company not in

malayalam on a well-defined siya or not

a well-defined set also

Inaba a null set or empty cell next we

will determine the number of elements or

what are the elements of a given cell

and plus B belonging at income in line

and B Longman elements a sunset or young

teen atomic netting cardinality so bag

atomic precedes a discussion ISA ISA

Hinman anata no mana Selita naquadah

natima encounters through the examples

Parimal a Manhattan kanuma bang ibig

sabihin amana ito so a toy human a

possible examples pneumatic eaten in

your Salmonella bro

salmon artists nahin eating it so IDI

differentiate nadine Shia is ASA okay

Anagha bang integers so foxy nominating

integers at the human a numbers number

of negative numbers of from negative

infinity zero up to positive infinity so

among a negative number zero and

positive numbers unka be lanza integers

next cool numbers suppose in a be

nothing whole numbers lag atomic CC

molasses 0 so from 0 1 to positive

infinity so you knew Monica be Lanza

whole numbers so coxinha be not equal

numbers well initial negative numbers so

0 nalang and positive numbers next

counting numbers or natural numbers

autonomy new manga numbers Na Nog see

similar Wonka bill and Ito I 1 up to net

a positive infinity so from the ride

itself County Sun battalion axis in

Muhammad belong so so 1 2 3 4 up to

positive infinity so mwall Anna do

young's 0 cap again mailroom 0 a big

Sabean who numbers young okay

next even numbers even numbers starts

with 2 4 6 8 10 and so on and so forth

it's like multiples of 2 it's like skip

counting by twos add numbers at an

Emanuel Ax numbers an accessible as a 1

followed by 3 5 7 9 d so yeah impeccable

even at odd number so the Padma

familiarize tiresome word source terms

NATO para Padma Heaton attention eben

aquellas example LM not in come on you

ibig sabihin another we have prime

numbers by Cena be nominating prime and

turning multiplier in your lung I 1 and

itself so halimbawa 2 & 2 we only have 1

times 2 to get a product of 2

I'm sorry 1 times 3 to get a product of

3 5 7 11 also soybean

also 17 also 19 so those are examples of

prime numbers

next composite numbers this ID number is

now Hindi LOM one in itself and Brad and

factor Cena had him bow-wow c4 and for

what so one times four by the time

acronym two times to see six before so

one times six Marin Shang two times

three

honey Bao was it well Marin Shang one

times 12 three and four twenty six so

those are examples of composite numbers

so 4 6 8 9 12 10 now why is it that we

do not have one okay always remember

that one is not a prime nor composite

why one is a special number so indicia

fabulous a prime nor composite numbers

because one is a special number next

perfect squares so pugs in a be

nominating perfect squares this idea

Prada at Omaha Prada nominal number

nominal de plana 10 by itself

halimbawa the number is 1 1 times 1 the

product is 1 therefore one is a perfect

square to 2 times 2 the product is for

therefore 4 is a perfect square so when

we are multiplying the number by itself

the product is school a perfect squares

another example 5 times 5 that is 25

therefore 25 is a perfect square also so

it is 649 81/100 because 110 times 10

next multiples multiples

it's like skip counting so if your ass

come tonight on fire give the multiples

of 3 so we will have 3 6 9 12 15

multiples of 5 5 10 15 20 so it's like

skip counting

and then factors factors these are

numbers which can be divided without

remainder so halimbawa factors of six so

what are the factors of six we have one

two three and six so when we are going

to multiply six by one the quotient is

six six divided 2 is 3 60 by 3 is 2 and

6 divided 6 is 1 so as you can see lahat

loom numbers now Jana the device would

not end well I'm not even remainder so

one patters of 6 1 2 3 & 6 are the

factors of 6

let's have pearls and a PvP okay so

Maranatha mana pitchers and I have here

a t-ball group by 3 so we have Group a

group B and Group C so I have here three

groups and we will try to group these

pictures by three according to its

classification characteristic or

category okay so let's start

okay so I have here for group a shoe

jacket cop for Group B we have a ball

doll and toy car for group C we have

orange mango and banana from the given

table group by three so for group a we

have shoe jacket and cup for group B

ball doll and toy car for a group C we

have mango orange and banana okay

now twenty bouncy doll is sama Xhosa

group a boy debunks issue is a Mufasa

group si puede bouncy banana exam I was

a group B and then young boy car is a

Mufasa group C so back it kiya Hindi not

in sit-up wedding is Amidon Hey so for

group a we have shoes jacket and

buckets Allah in Makaha sama because

group a our set of objects that can be

worn so it is a good satin oh not in

Kalina from bucket in denied in wedding

is a monument of young mango young toy

car because group a are all objects that

can be born next for group B we have

ball doll and toy car back is in Makaha

sama because Group B is a set of toys

and then for group C this is a set of

fruits now these three are considered

set so these three are all examples of

set Etherington atomic nothing said said

topic maroon sedan is on classification

or characteristics or category so Union

can you consider nothing as I said I

know GABA answer

so a set is a group or collection of

objects so it or a group or nappin

eczema's among objects of course with

the same characteristic at a quarry or

classification remember that I said is

named using capital letters of a guy an

example coca Nina young group named Mila

set a set B and set C are capital

letters so GU mamita phone on capital

letters Casa Hindi puede and small cap

exactly named dhyanam said now each

object in a set is called a member or an

element of a set so an anatomic not

induce a megalomania halimbawa sassette

e de la monja i jacket cup and shoe so

young Pat Luna you on unity not about

Nadine element so intelligence among our

members or objects Noma fakey Tomasulo

Abner a son said I element what is an

element so this is our symbol for

element and this is our symbol for not

an element sorting nguyen pakka ha ha

you just have to put slash but the

things are not an element pero para who

lung Shan Mei / legume not an element so

the pot LM not in company char got a

meetin okay let's have an example set a

is a set of school days in a week so

unabating school days in a week you man

add all anime path so we have Monday

Tuesday Wednesday Thursday and Friday

so a to Monday Tuesday Wednesday

Thursday and Friday are called members

or elements of a given set so Adrienne

Tina table agentic element so pertinent

Ohio what are the elements of set a

Monday Tuesday Wednesday Thursday and

Friday

next pan open attending a gamete and

symbol K song symbol so halimbawa I have

here Monday Monday how do we read is is

an element of set a gazelle from the

given example on Monday is personal

school days so Monday is an element of

set a Thursday is an element or set a

now obviously liniment I am a person on

Sunday so sunday is not an element of

set a so take note of the symbol used

next Saturday is not an element of set E

a next sub P is a set of counting

numbers less than five so take note of

the word less than PAC Cena be nothing

less than MASMA Bubba mask my Barbossa 5

so a noona only 10 counting numbers and

Nexus Imola Annina Lex is in Milazzo 1k

so I know I know your mama counting

numbers the MASMA Barbossa 5 so we have

1 2 3 4 okay so Adam 1 2 3 4 ante natal

what nothing elements num counting

numbers less than 5 next set B is the

set of primary colors so an undo by you

mono primary colors we have yellow red

blue

so a tone yellow red and blue are the

elements of set B which is the set of

primary colors

okay let's have more example I have here

set a even numbers set be the set of odd

numbers set C the set of counting

numbers okay so Chi Chi Yong einen

sinabi cocaina even numbers 2 4 6 add

numbers 1 3 5 7 and set C counting

numbers starts with 1 hey so fill in the

blank with element or not an element

okay so - is it an element or not an

element of set a pontiff is a a I'm sabe

am AI even numbers and - by even numbers

yes so therefore that is an element

thanks 7 is 7 an element or not an

element of set C and set C I counting

numbers so I'm 7 bar I could consider it

as a counting number yes so that is an

element next negative 2 is negative 2 an

element or not an element of set C a

negative 2 bar I guess I'm us among

accounting numbers No so therefore this

is not an element because negative 2 is

an integer next it is an is not an

element of set B because it is not an

even rather an odd number so I'm eat I

hindi esha add number so therefore this

is not an element next 3 M 3 bar I

element or not an element of set D but I

cannot in a set B sub a add numbers so

um 3 by at number yes so this is an

element and the last one we

five-five is blank offset a and fiber I

even number no so this is not an element

all right let's talk about well-defined

set the a no Bernadine Monell among well

define or not well-defined

example I have here such a the set of

primary colors

eeny Meeny biome primary colors might be

began at end of course we have red blue

and yellow

so therefore this is considered well

defined set set a is a well defined set

max set B set of beautiful girls in

school okay this example or this set is

not considered well defined so this is

not a well-defined set why because of

the word beautiful okay

so per column bagua Paris offend maganda

she say Oh me mass maganda or Paris know

Hindi she maganda so ibig sabihin

it's not well defined in d mu not in

Shama IPP guy nah Perry Perry hotel so

ibig sabihin

this is not a well-defined set okay

mallamma nothing will define sure if the

adjective is present in a given set so

detour you beautiful that makes the set

not well defined so yeah not attend

anything next set C set of months in a

year so we all know that that is from

January to December so this is a well

defined set set the set of a popular

outdoor so this is again not a

well-defined set because of the word

popular next e set of excellent singers

so this is also not well defined because

of the word excellent

what if for me sang Macaulay Gustav on

singers I'm Madeleine comenta Paris I

own in there so that makes it not

well-defined set up percent F we have

set of even numbers so even numbers 2 4

6 8 10 so this is I will define set

next empty set or a null set a set with

no members or elements so hapa gang said

more ìwell um members or elements

Wallachian Lemann ibig sabihin that is

an empty set or an asset Samaritan

symbol Nagina gamma John for empty said

it looks like a bracket for it now said

it looks like a oval with a slash so

again we can make use of symbol for

empty set and null set

what are the examples set of triangles

with foresight so set a is the set of

triangles with four sides so Marin

County but even Placid and triangle is

mentally cui if we angle our triangle

equilateral triangles isosceles scalene

right obtuse triangle acute triangle so

Marin Tyagi but if I'm passing and try

and get now Marin Bank triangle Nam my

four sites of course wallah

so this is an example of empty set or

Nelson course of a beginning is in at

all give the set of triangles with

foresight you just have to answer empty

set or null set next set B is the set of

months in the year start with B so Marin

bong month name now manga mines the

Nexus I'm iliza be voila

we only have three a M s.o.b I know n B

well a time B so if it's a behind this

is also a now set or empty set set C set

of all numbers less than zero we all

know that a whole number starts with

zero so Marin Popham MASMA Bob us a zero

voila so the

is also an example of empty set or an

asset

neck's cardinality this refers to the

number of elements in a given set so

apart engineering in a man I belong

peanut bebe Lancome Elana elements that

is already cardinality we are already

talking about cardinality it is denoted

by the symbol small letter n again it

must be small how EE this cardinality of

set a so it is written as small letter N

and then the name of the set enclosed by

parentheses again the symbol for

cardinality small letter N and then the

name of the cell and close by the

parentheses so this is an example hey so

I have here set a set of primary colors

so for set a we have yellow red blue now

can t not I know my cardinality because

a big number

B elements so for the set of primary

colors we have yellow red and blue we

have three elements right so we will be

writing cardinality of set a is equal to

3 so 3 is and number 3 is the number of

elements so small letter n the name of

the set enclosed by the parentheses and

then the number of elements another

example school days in a week so for set

B we have Mondays to Fridays so how many

elements do we have 1 2 3 4 5 so we have

cordiality upset be ignored it is

already be because the name of the set

is B cardinality of set B is equal to 5

because we have five elements mere

entire mood among elements Nana Paula

orb

sassette B

now what if there is no elements in a

given cell what will be its cardinality

example set of days in a week starts

with a Maren bang around an axis in

Milazzo a Monday that is M Tuesday

Thursday that is T Wednesday is w Friday

is a Saturday and Sunday is s so Maren

back so a party maintenant cardinality I

know some of you will answer and this a

or Nancy but this is wrong

okay why remember that a final appeal

the first two the number of elements you

should have written the number pay some

illaallah gain at and a number belong

come on peanut and on I what are the

elements of days in a week starts with a

a Tom Petty nothing is a good empty set

or now said cassy walla Hanuman illallah

gain elements pair oh come on tonight on

oh my cardinality since it refers to the

number of elements belong so that button

illallah gain a tonight the Heidi

nullity upset a is equal to 0 K remember

that solely think oh come on T not a

known I I know I know among elements you

should answer empty set or now said

paraffin antimatter know my cardinality

so a big Sabine belong so an elegant not

in I 0

that's all for this video thank you and

don't forget to Like subscribe and click

the build button again this is wall man