Shadowing-Übung: SET Notations | Mathematics: IGCSE, GCSE & O Level (CIE/CAIE, Edexcel, AQA, OCR) - Englisch Sprechen Lernen mit Video

Übungsmodus wählen

Jeder Modus öffnet einen Übungsraum im Vollbild.

122 Sätze

Wenn Sätze zu kurz oder zu lang sind, klicke auf Edit, um sie anzupassen.

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.

App herunterladen

Alles, was du zum fließenden Sprechen brauchst

KI-AussprachebewertungJeder Satz bewertet

IPA-TrainingJeden Laut meistern

WortschatzBaue deinen Wortschatz auf

VokabelspielSpielend lernen

QR scannen

Download on theApp Store Get it onGoogle Play

FOR YOU

Empfohlenes Video

14 Sätze

Wortschatz und Sprechhinweise zu dieser Lektion

Dieses Video enthält 121 Sätze und 1354 Wörter zum Nachsprechen. Der gesprochene Teil dauert 11:55. Der Sprecher spricht gleichmäßig mit etwa 114 Wörtern pro Minute – ein angenehmes Tempo fürs Shadowing. Nur 79 % der Wörter gehören zu den 3.000 häufigsten im Englischen, der Wortschatz ist also anspruchsvoll.

Wichtiger Wortschatz in diesem Video

15 weniger häufige Wörter aus dem Video, mit Aussprache und Bedeutung:

element /ˈɛləmənt/ (Substantiv) — Element. 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/ (Substantiv) — Kreuzung, Straßenkreuzung. The junction of two (or more) paths, streets, highways, or other thoroughfares.
subset /ˈsʌbˌsɛt/ (Substantiv) — Untermenge, Teilmenge. A set A such that every element of A is also an element of S.
symbol /ˈsɪmbəl/ (Substantiv) — Symbol, Zeichen. A character or glyph representing an idea, concept or object.
universal /ˌjunəˈvɜɹs(ə)l/ (Adjektiv) — allgemein, Allgemein-. Of or pertaining to the universe.
brace /bɹeɪs/ (Substantiv) — Klammer, Spange. A curved instrument or handle of iron or wood, for holding and turning bits, etc.; a bitstock.
mathematics /mæθ(.ə)ˈmæt.ɪks/ (Substantiv) — Mathematik. An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them.
combine /kəmˈbaɪn/ (Verb) — kombinieren, verbinden. To bring (two or more things or activities) together; to unite.
subscribe /səbˈskɹaɪb/ (Verb) — abonnieren. To write (one’s name) at the bottom of a document; to sign (one's name).
motivate /ˈmoʊ.tɪ.veɪt/ (Verb) — motivieren. To provide someone with an incentive to do something; to encourage; to actuate.
involve /ɪnˈvɑlv/ (Verb) — verbunden sein (mit), mit sich bringen. To have (something) as a component or a related part; to comprise, to include.
dive /daɪv/ (Verb) — tauchen. To swim under water.
tricky /ˈtɹɪk.i/ (Adjektiv) — schwierig, heikel. Hard to deal with, complicated.
bracket /ˈbɹækɪt/ (Substantiv) — Winkel, Träger. A fixture attached to a wall to hold up a shelf.
alternatively /ɔlˈtɝ.nə.tɪv.li/ (Adverb) — alternativ, andernfalls. in an alternative way

Phrasal Verbs, die du hören wirst

look at (Verb) — schauen. To observe or watch.
look for (Verb) — suchen. To seek.
make for (Verb) — sich zusteuern auf, zustreben. To set out to go (somewhere); to move towards.

Aussprache, auf die du achten solltest

Der Sprecher verwendet 8 Kurzformen und abgeschwächte Formen, zum Beispiel I'd, we're, don't. Sprich sie in der kurzen Form, so wie du sie hörst.

Die Laute „sh“ und „zh“: intersection /ˈɪntəɹˌsɛkʃən/, notation /noʊˈteɪʃən/, foundational /faʊnˈdeɪ.ʃə.nəl/
Lange Wörter – auf die Betonung achten: intersection /ˈɪntəɹˌsɛkʃən/, universal /ˌjunəˈvɜɹs(ə)l/, mathematics /mæθ(.ə)ˈmæt.ɪks/, alternatively /ɔlˈtɝ.nə.tɪv.li/, foundational /faʊnˈdeɪ.ʃə.nəl/

So übst du mit diesem Video

Höre dir das ganze Video einmal an, ohne zu sprechen, und notiere die Wörter, die du nicht kennst.
Sprich Satz für Satz in normaler Geschwindigkeit nach und wiederhole jeden, bis dein Rhythmus zum Sprecher passt.
Nimm dich auf und vergleiche mit dem Original; achte dabei auf Wörter wie element, intersection, subset.

Grammatik in diesem Video

Die Strukturen, die der Sprecher am häufigsten verwendet, mit den genauen Worten aus dem Video:

Struktur	Im Video
Bedingungssätze if + Satz, will/would + Verb – eine Bedingung und ihre Folge	If it does, I'd super
Passiv be + Partizip Perfekt – wichtig ist, was geschieht, nicht wer es tut	is made · are called · can be described
Relativsätze who / which + Satz – eine Zusatzinformation über eine Person oder Sache	objects, which are · elements which are

Was ist die Shadowing-Technik?

Shadowing ist eine wissenschaftlich fundierte Sprachlerntechnik, die ursprünglich für die professionelle Dolmetscherausbildung entwickelt und durch den Polyglotten Dr. Alexander Arguelles populär gemacht wurde. Die Methode ist einfach aber wirkungsvoll: Du hörst englisches Audio von Muttersprachlern und wiederholst es sofort laut — wie ein Schatten, der dem Sprecher mit nur 1–2 Sekunden Verzögerung folgt. Anders als passives Hören oder Grammatikübungen zwingt Shadowing dein Gehirn und deine Mundmuskulatur, gleichzeitig echte Sprachmuster zu verarbeiten und zu reproduzieren. Studien zeigen, dass es Aussprachegenauigkeit, Intonation, Rhythmus, verbundene Sprache, Hörverständnis und Sprechflüssigkeit signifikant verbessert — was es zu einer der effektivsten Methoden für die IELTS Speaking-Vorbereitung und reale englische Kommunikation macht.

Shadowing-Technik: die vollständige Schritt-für-Schritt-Anleitung lesen →

Shadowing-Übung: SET Notations | Mathematics: IGCSE, GCSE & O Level (CIE/CAIE, Edexcel, AQA, OCR) - Englisch Sprechen Lernen mit Video

Übungsmodus wählen

App herunterladen

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?

Wortschatz und Sprechhinweise zu dieser Lektion

Wichtiger Wortschatz in diesem Video

Phrasal Verbs, die du hören wirst

Aussprache, auf die du achten solltest

So übst du mit diesem Video

Grammatik in diesem Video

Was ist die Shadowing-Technik?