Практика Shadowing: SET Notations | Mathematics: IGCSE, GCSE & O Level (CIE/CAIE, Edexcel, AQA, OCR) - Изучайте разговорный английский по видео

Выберите режим практики

Каждый режим открывает полноэкранную комнату практики.

122 предложений

Если предложения слишком короткие или длинные, нажмите Edit, чтобы их изменить.

Hi everyone!

Welcome to Plaid Academy.

I really hope this video helps you out.

If it does, I'd super appreciate it if you could subscribe to my channel, give this video a like, share it with your friends, and leave a positive comment.

Your support really keeps me motivated to create more great videos

for you hey everyone in this video we're going to dive

into the basics of sets we'll cover what a set is the notations of sets and how to perform set operations

now if you're studying for your ig cse gcse or o level exams with cambridge international Pearson at Excel,

AQA, or OCR, this video is made for you.

It's also essential foundational knowledge for anyone heading into higher -level math.

I hope you have fun learning and start loving math as much as I do.

Let's get started.

A set is a collection of objects, which are called the elements or members of the set.

These objects can be numbers, animals, fruits, colors, in fact, anything you can imagine.

A set can be described in two ways, by listing all its members or by giving a rule to describe them.

In both cases, the list or rule is always enclosed in braces or curly brackets.

For example, here is a set B shown by listing all its members,

2, 4, 6, 8, enclosed in braces.

Alternatively, this same set B can be described by a rule,

the positive even numbers less than 10, also enclosed in braces.

Both of these represent the exact same collection of objects.

Next, let's talk about set notation.

We're going to cover the symbols for the number of elements in a set, is a member of, the empty set,

the universal set, subsets, complements, intersections, and unions.

The number of elements or members in the set B is denoted by this symbol.

Using our sets from before, the number of elements in set B is 4.

This symbol means is a member of, or is an element of, and the symbol means is not a member of.

In the above example, 2 is a member of B,

but 3 is not a member of Next,

let's talk about empty sets and universal sets.

This symbol, or this symbol, is used to represent the empty set, or the null set.

For example, if the set B equals days of the week starting with P,

then B is empty set because there are no members in set B.

Therefore, the number of elements in set B is zero.

Now, the universal set is denoted by this symbol.

The universal set contains all the elements being considered in a particular problem.

For example, if our universal set is days of the week, we would list all members as Monday,

Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.

Next, let's talk about subsets and complements.

This symbol, or this symbol, means is a subset of.

If set A is a subset of B, it means that every member of A is also a member of B.

For example, let's look at set B equals 2, 4, 6.

The all possible subsets of B are set of 2, set of 4, set of 6,

set of 2, 4, set of 2, 6, set of 4, 6, and set of 2, 4, 6.

And don't forget, the empty set is also a subset of B.

The empty set is always a subset of every set.

Now, the complement of set A is denoted by this symbol.

It is the set of all elements in the universal set that are not in A.

For example, if our universe is days of the week, and set A contains days starting with T, which is Tuesday, Thursday.

Therefore, the complement of set A is Monday, Wednesday, Friday, Saturday, Sunday.

Next, let's talk about intersection and union.

The intersection of sets is denoted by this symbol.

The intersection of A and B is the set of elements which are in both A and B.

If set A is the positive integers that less than 10 and set B is 2, 3, 7, 11, 14, 25,

therefore the intersection of A and B is 2, 3, 7.

Now, the union of sets is denoted by this symbol.

The union of A and B is a set of elements which are in A or B or both.

Using our sets from before, the union of A and B is 1, 2, 4, 5, 6, 7,

8, 9, 11, 14, 25.

Next, let's talk about how to perform set operations.

If the universal set is 1, 2, 3, 4, 5, 6,

7, 8, 9, 10, we have three sets within it.

Set A is 1, 3, 5, set B is 3,

4, 5, and set C is 1, 4, 10.

Now, let's find the complement of set A.

The complement of set A is all elements in the universal set that are not in A.

So we remove the members of set A, which are 1, 3, 5, from the universal set.

Therefore, the complement of A is 2, 4, 6, 7, 8, 9, 10.

Next, let's find the union of B and C.

The union of B and C is the set of elements which are in A or B or both.

Combining them gives us B union C.

Therefore, the union of B and C is 1, 3, 4, 5, 10.

Finally, find the intersection of A and B.

The intersection of A and B is the set of elements which are in both A and B.

Looking at our lists, 3 and 5 appear in both.

Therefore, A intersection B is 3, 5.

Next, let's look at operations involving three sets.

Using our sets from before, first find the intersection of A, B, and C.

This is the set of elements that are in all three sets at the same time.

If we check our lists, there isn't a single number that appears in A, B, and C.

Therefore, A intersection B intersection C is the empty sets.

Now, let's find the number of elements in the complement of B and then intersection with A, then union with C.

This looks tricky, so let's do it step by step.

Step 1.

Find the complement of B.

The complement of set B is all elements in the universal set that are not in B.

We remove 3, 4, and 5 from the universal set.

Therefore, the complement of B is 1, 2, 6, 7, 8, 9, 10.

Step 2.

Find the intersection of the complement of B and A.

The intersection of complement of B and A is the set of elements

which are in both the complement of B and A.

We look for elements that are in our new list and in set A.

The only number in both is 1.

Therefore, the intersection of the complement of B and A is 1.

Step 3.

Find the union of that result with set C.

The union of our result set and set C is the set of elements which are in 1, or C, or both.

We take our result set, 1, and combine it with everything in set C, 1, 4, 10.

100

Therefore, the complement of B.. intersection A and union C is 1 4 10.

101

Step 4.

102

Find the number of elements, since the number of elements in the complement of B intersection A and union C is 3.

103

Next, let's check your understanding of set notation.

104

Using our sets from before, state whether the following statements are true or false.

105

First, 5 is a member of B.

106

This is true because 5 is an individual element found inside set Second,

107

the set of 1, 5 is members of A.

108

This is false.

109

While 1 and 5 are elements of A, the set of 1, 5 is a subset of A, not a member.

110

Third, set A is a subset of C.

111

This is false.

112

For A to be a subset of C, every element in A must also be in C.

113

Since 3 and 5 are in A but not in C, A is not a subset.

114

Fourth, 4 -5 is a subset of B.

115

This is false.

116

The notation is wrong.

117

The numbers 4 and 5 are just a list of elements of B.

118

To represent a subset, they must be enclosed in braces to create a set, 4 -5.

119

Once you add the braces, 4 -5 is a subset of B would be true.

120

I really hope this video helps you out.

121

If it does, I'd super appreciate it if you could subscribe to my channel, give this video a like, share it with your friends, and leave a positive comment.

122

Your support really keeps me motivated to create more great videos for you.

Скачать приложение

Всё для свободной речи

ИИ-оценка произношенияОценка каждой фразы

Практика IPAОсвойте каждый звук

СловарьСоберите свой словарный запас

Игра со словамиУчитесь играя

Сканировать QR

Download on theApp Store Get it onGoogle Play

FOR YOU

Лексика и советы по произношению к этому уроку

В этом видео 121 предложений и 1354 слов для шедоуинга. Речь длится 11:55. Говорящий держит ровный темп — около 114 слов в минуту, удобный для шедоуинга. Только 79% слов входят в 3000 самых частых слов английского языка, поэтому лексика сложная.

Ключевая лексика этого видео

15 менее частых слов из видео с произношением и значением:

element /ˈɛləmənt/ (существительное) — элеме́нт, звено́. One of the simplest or essential parts or principles of which anything consists, or upon which the constitution or fundamental powers of anything are based.
intersection /ˈɪntəɹˌsɛkʃən/ (существительное) — перекрёсток. The junction of two (or more) paths, streets, highways, or other thoroughfares.
complement /ˈkɑmpləmənt/ (существительное) — дополне́ние до прямо́го угла́. The totality, the full amount or number which completes something.
subset /ˈsʌbˌsɛt/ (существительное) — подмно́жество. A set A such that every element of A is also an element of S.
symbol /ˈsɪmbəl/ (существительное) — си́мвол, знак. A character or glyph representing an idea, concept or object.
universal /ˌjunəˈvɜɹs(ə)l/ (прилагательное) — вселе́нский, косми́ческий. Of or pertaining to the universe.
brace /bɹeɪs/ (существительное) — скоба́, скре́па. A curved instrument or handle of iron or wood, for holding and turning bits, etc.; a bitstock.
mathematics /mæθ(.ə)ˈmæt.ɪks/ (существительное) — матема́тика. An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them.
combine /kəmˈbaɪn/ (глагол) — комбини́ровать, скомбини́ровать. To bring (two or more things or activities) together; to unite.
subscribe /səbˈskɹaɪb/ (глагол) — подпи́сывать, подписа́ть. To write (one’s name) at the bottom of a document; to sign (one's name).
motivate /ˈmoʊ.tɪ.veɪt/ (глагол) — мотиви́ровать. To provide someone with an incentive to do something; to encourage; to actuate.
involve /ɪnˈvɑlv/ (глагол) — каса́ться, косну́ться. To have (something) as a component or a related part; to comprise, to include.
dive /daɪv/ (глагол) — ныря́ть, нырну́ть. To swim under water.
tricky /ˈtɹɪk.i/ (прилагательное) — каверзны́й, щекотли́вый. Hard to deal with, complicated.
bracket /ˈbɹækɪt/ (существительное) — кронште́йн, подпо́рка. A fixture attached to a wall to hold up a shelf.

Фразовые глаголы, которые вы услышите

talk about (глагол) — ну и, вот э́то. Used to draw attention to the speaker's characterization of someone or something.
look for (глагол) — иска́ть, поиска́ть. To seek.
make for (глагол) — направля́ться, напра́виться. To set out to go (somewhere); to move towards.

Произношение, на которое стоит обратить внимание

Говорящий использует 8 сокращённых и редуцированных форм, например I'd, we're, don't. Произносите их коротко, так, как слышите.

Звуки «sh» и «zh»: intersection /ˈɪntəɹˌsɛkʃən/, notation /noʊˈteɪʃən/, foundational /faʊnˈdeɪ.ʃə.nəl/
Длинные слова — следите за ударением: intersection /ˈɪntəɹˌsɛkʃən/, universal /ˌjunəˈvɜɹs(ə)l/, mathematics /mæθ(.ə)ˈmæt.ɪks/, alternatively /ɔlˈtɝ.nə.tɪv.li/, foundational /faʊnˈdeɪ.ʃə.nəl/

Как заниматься с этим видео

Прослушайте всё видео один раз молча и выпишите незнакомые слова.
Повторяйте предложение за предложением на обычной скорости, пока ваш ритм не совпадёт с ритмом говорящего.
Запишите себя и сравните с оригиналом, обращая внимание на такие слова, как element, intersection, complement.

Грамматика в этом видео

Конструкции, которые говорящий использует чаще всего, с точными словами из видео:

Конструкция	В видео
Условные предложения if + предложение, will/would + глагол — условие и его результат	If it does, I'd super
Пассивный залог be + причастие прошедшего времени — важно, что происходит, а не кто это делает	is made · are called · can be described
Придаточные определительные who / which + предложение — уточнение о человеке или предмете	objects, which are · elements which are

Что такое техника Shadowing?

Shadowing — это научно обоснованная техника изучения языка, изначально разработанная для подготовки профессиональных переводчиков и популяризированная полиглотом доктором Александром Аргуэльесом. Метод прост, но эффективен: вы слушаете аудио на английском от носителей языка и немедленно повторяете вслух — как тень, следующая за говорящим с задержкой в 1–2 секунды. В отличие от пассивного прослушивания или грамматических упражнений, Shadowing заставляет мозг и мышцы рта одновременно обрабатывать и воспроизводить реальные речевые паттерны. Исследования показывают, что это значительно улучшает точность произношения, интонацию, ритм, связную речь, понимание на слух и беглость речи — что делает его одним из самых эффективных методов для подготовки к IELTS Speaking и реального общения на английском.

Техника шедоуинга: читать полное пошаговое руководство →

Практика Shadowing: SET Notations | Mathematics: IGCSE, GCSE & O Level (CIE/CAIE, Edexcel, AQA, OCR) - Изучайте разговорный английский по видео

Выберите режим практики

Скачать приложение

Рекомендуемое видео

FCE speaking part 1 studing

KS3 Chemistry - The periodic Table

The 8 Parts of Speech in English Grammar (+ Free PDF & Quiz)

IB EXPLAINED | everything you NEED TO KNOW about IB

Lec 1 | MIT 18.06 Linear Algebra, Spring 2005

WHAT ARE NATURAL NUMBERS?

Unit 2: Being young | Collins - Listening for IELTS.

NEW- Micro Unit 1 Summary- Basic Economic Concepts

The category of G-Sets

Anand Kumar Super 30 | Engineerzzz

What is YOUR English level? Take this test!

7 Cấp Độ Toán Học: Bạn Đang Ở Đâu?

Лексика и советы по произношению к этому уроку

Ключевая лексика этого видео

Фразовые глаголы, которые вы услышите

Произношение, на которое стоит обратить внимание

Как заниматься с этим видео

Грамматика в этом видео

Что такое техника Shadowing?