INTRODUCTION TO SETS || GRADE 7 MATHEMATICS Q1
Summary
TLDRThis 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
- đ Introduction to sets and their various concepts, including well-defined and not well-defined sets.
- đą Explanation of different types of numbers such as integers, whole numbers, counting numbers, even numbers, odd numbers, prime numbers, composite numbers, and perfect squares.
- âïž Multiples and factors are discussed with examples, highlighting how numbers can be divided without remainders.
- đ Grouping objects into sets based on their characteristics, such as clothing items, toys, and fruits.
- đ Sets are named using capital letters, and each object in a set is called a member or an element.
- đ Symbols used to denote elements and non-elements in a set, with examples of well-defined and not well-defined sets.
- đ Empty sets (null sets) are explained, including how to denote them and examples like triangles with four sides and months starting with 'B'.
- đą Cardinality refers to the number of elements in a given set, denoted by 'n'. Examples of calculating cardinality are provided.
- â Cardinality of empty sets is always zero, as they contain no elements.
- đœïž 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
đ 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.
đą 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.
đ 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.
đ 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.
𧩠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.
đ 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.
â 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.
Mindmap
Keywords
đĄSet
đĄElement
đĄWell-defined set
đĄEmpty set
đĄCardinality
đĄPrime numbers
đĄComposite numbers
đĄEven numbers
đĄOdd numbers
đĄPerfect squares
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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possible examples pneumatic eaten in
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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 ĂŹwell 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
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