Shadowing Practice: SET Notations | Mathematics: IGCSE, GCSE & O Level (CIE/CAIE, Edexcel, AQA, OCR) - Learn English Speaking with Video

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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.

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

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Step 4.

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

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

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

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First, 5 is a member of B.

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

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the set of 1, 5 is members of A.

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This is false.

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

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Third, set A is a subset of C.

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This is false.

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

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

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Fourth, 4 -5 is a subset of B.

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This is false.

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The notation is wrong.

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

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

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

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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.

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14 sentences

Vocabulary and speaking notes for this lesson

This video has 121 sentences and 1354 words to shadow. The speech runs for 11:55. The speaker talks at a steady 114 words per minute, a comfortable pace for shadowing. Only 79% of the words are among the 3,000 most common in English, so the vocabulary is demanding.

Key vocabulary in this video

15 less common words from the video, with pronunciation and meaning:

element /ˈɛləmənt/ (noun) — 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/ (noun) — The junction of two (or more) paths, streets, highways, or other thoroughfares.
complement /ˈkɑmpləmənt/ (noun) — The totality, the full amount or number which completes something.
subset /ˈsʌbˌsɛt/ (noun) — A set A such that every element of A is also an element of S.
symbol /ˈsɪmbəl/ (noun) — A character or glyph representing an idea, concept or object.
universal /ˌjunəˈvɜɹs(ə)l/ (adjective) — Of or pertaining to the universe.
brace /bɹeɪs/ (noun) — A curved instrument or handle of iron or wood, for holding and turning bits, etc.; a bitstock.
mathematics /mæθ(.ə)ˈmæt.ɪks/ (noun) — An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them.
combine /kəmˈbaɪn/ (verb) — To bring (two or more things or activities) together; to unite.
subscribe /səbˈskɹaɪb/ (verb) — To write (one’s name) at the bottom of a document; to sign (one's name).
motivate /ˈmoʊ.tɪ.veɪt/ (verb) — To provide someone with an incentive to do something; to encourage; to actuate.
involve /ɪnˈvɑlv/ (verb) — To have (something) as a component or a related part; to comprise, to include.
exam /ɪɡˈzæm/ (verb) — Shortened form of examine
dive /daɪv/ (verb) — To swim under water.
tricky /ˈtɹɪk.i/ (adjective) — Hard to deal with, complicated.

Phrasal verbs you will hear

talk about (verb) — Used to draw attention to the speaker's characterization of someone or something.
look at (verb) — To observe or watch.
look for (verb) — To seek.
make for (verb) — To set out to go (somewhere); to move towards.

Pronunciation to watch

The speaker uses 8 contractions and reduced forms, such as I'd, we're, don't. Say them the short way, as you hear them.

The “sh” and “zh” sounds: intersection /ˈɪntəɹˌsɛkʃən/, notation /noʊˈteɪʃən/, foundational /faʊnˈdeɪ.ʃə.nəl/
Long words — get the stress right: intersection /ˈɪntəɹˌsɛkʃən/, universal /ˌjunəˈvɜɹs(ə)l/, mathematics /mæθ(.ə)ˈmæt.ɪks/, alternatively /ɔlˈtɝ.nə.tɪv.li/, foundational /faʊnˈdeɪ.ʃə.nəl/

How to practise with this video

Listen to the whole video once without speaking and note the words you do not know.
Shadow it sentence by sentence at normal speed, repeating each one until your rhythm matches the speaker.
Record yourself and compare with the original, paying attention to words like element, intersection, complement.

Grammar in this video

The structures the speaker uses most, with the exact words from the video:

Structure	In the video
Conditional sentences if + clause, will/would + verb — a condition and its result	If it does, I'd super
Passive voice be + past participle — the focus is on what happens, not who does it	is made · are called · can be described
Relative clauses who / which + clause — extra information about a person or thing	objects, which are · elements which are

What is the Shadowing Technique?

Shadowing is a science-backed language learning technique originally developed for professional interpreter training and popularized by polyglot Dr. Alexander Arguelles. The method is simple but powerful: you listen to native English audio and immediately repeat it out loud — like a shadow following the speaker with just a 1–2 second delay. Unlike passive listening or grammar drills, shadowing forces your brain and mouth muscles to simultaneously process and reproduce real speech patterns. Research shows it significantly improves pronunciation accuracy, intonation, rhythm, connected speech, listening comprehension, and speaking fluency — making it one of the most effective methods for IELTS Speaking preparation and real-world English communication.

Shadowing technique: read the full step-by-step guide →

Shadowing Practice: SET Notations | Mathematics: IGCSE, GCSE & O Level (CIE/CAIE, Edexcel, AQA, OCR) - Learn English Speaking with Video

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Vocabulary and speaking notes for this lesson

Key vocabulary in this video

Phrasal verbs you will hear

Pronunciation to watch

How to practise with this video

Grammar in this video

What is the Shadowing Technique?