Pratica di Shadowing: SET Notations | Mathematics: IGCSE, GCSE & O Level (CIE/CAIE, Edexcel, AQA, OCR) - Impara a parlare inglese con i video
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Hi everyone!
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Welcome to Plaid Academy.
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I really hope this video helps you out.
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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.
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Your support really keeps me motivated to create more great videos
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for you hey everyone in this video we're going to dive
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into the basics of sets we'll cover what a set is the notations of sets and how to perform set operations
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now if you're studying for your ig cse gcse or o level exams with cambridge international Pearson at Excel,
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AQA, or OCR, this video is made for you.
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It's also essential foundational knowledge for anyone heading into higher -level math.
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I hope you have fun learning and start loving math as much as I do.
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Let's get started.
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A set is a collection of objects, which are called the elements or members of the set.
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These objects can be numbers, animals, fruits, colors, in fact, anything you can imagine.
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A set can be described in two ways, by listing all its members or by giving a rule to describe them.
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In both cases, the list or rule is always enclosed in braces or curly brackets.
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For example, here is a set B shown by listing all its members,
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2, 4, 6, 8, enclosed in braces.
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Alternatively, this same set B can be described by a rule,
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the positive even numbers less than 10, also enclosed in braces.
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Both of these represent the exact same collection of objects.
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Next, let's talk about set notation.
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We're going to cover the symbols for the number of elements in a set, is a member of, the empty set,
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the universal set, subsets, complements, intersections, and unions.
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The number of elements or members in the set B is denoted by this symbol.
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Using our sets from before, the number of elements in set B is 4.
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This symbol means is a member of, or is an element of, and the symbol means is not a member of.
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In the above example, 2 is a member of B,
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but 3 is not a member of Next,
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let's talk about empty sets and universal sets.
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This symbol, or this symbol, is used to represent the empty set, or the null set.
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For example, if the set B equals days of the week starting with P,
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then B is empty set because there are no members in set B.
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Therefore, the number of elements in set B is zero.
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Now, the universal set is denoted by this symbol.
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The universal set contains all the elements being considered in a particular problem.
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For example, if our universal set is days of the week, we would list all members as Monday,
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Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.
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Next, let's talk about subsets and complements.
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This symbol, or this symbol, means is a subset of.
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If set A is a subset of B, it means that every member of A is also a member of B.
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For example, let's look at set B equals 2, 4, 6.
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The all possible subsets of B are set of 2, set of 4, set of 6,
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set of 2, 4, set of 2, 6, set of 4, 6, and set of 2, 4, 6.
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And don't forget, the empty set is also a subset of B.
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The empty set is always a subset of every set.
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Now, the complement of set A is denoted by this symbol.
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It is the set of all elements in the universal set that are not in A.
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For example, if our universe is days of the week, and set A contains days starting with T, which is Tuesday, Thursday.
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Therefore, the complement of set A is Monday, Wednesday, Friday, Saturday, Sunday.
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Next, let's talk about intersection and union.
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The intersection of sets is denoted by this symbol.
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The intersection of A and B is the set of elements which are in both A and B.
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If set A is the positive integers that less than 10 and set B is 2, 3, 7, 11, 14, 25,
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therefore the intersection of A and B is 2, 3, 7.
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Now, the union of sets is denoted by this symbol.
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The union of A and B is a set of elements which are in A or B or both.
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Using our sets from before, the union of A and B is 1, 2, 4, 5, 6, 7,
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8, 9, 11, 14, 25.
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Next, let's talk about how to perform set operations.
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If the universal set is 1, 2, 3, 4, 5, 6,
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7, 8, 9, 10, we have three sets within it.
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Set A is 1, 3, 5, set B is 3,
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4, 5, and set C is 1, 4, 10.
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Now, let's find the complement of set A.
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The complement of set A is all elements in the universal set that are not in A.
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So we remove the members of set A, which are 1, 3, 5, from the universal set.
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Therefore, the complement of A is 2, 4, 6, 7, 8, 9, 10.
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Next, let's find the union of B and C.
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The union of B and C is the set of elements which are in A or B or both.
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Combining them gives us B union C.
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Therefore, the union of B and C is 1, 3, 4, 5, 10.
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Finally, find the intersection of A and B.
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The intersection of A and B is the set of elements which are in both A and B.
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Looking at our lists, 3 and 5 appear in both.
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Therefore, A intersection B is 3, 5.
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Next, let's look at operations involving three sets.
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Using our sets from before, first find the intersection of A, B, and C.
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This is the set of elements that are in all three sets at the same time.
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If we check our lists, there isn't a single number that appears in A, B, and C.
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Therefore, A intersection B intersection C is the empty sets.
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Now, let's find the number of elements in the complement of B and then intersection with A, then union with C.
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This looks tricky, so let's do it step by step.
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Step 1.
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Find the complement of B.
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The complement of set B is all elements in the universal set that are not in B.
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We remove 3, 4, and 5 from the universal set.
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Therefore, the complement of B is 1, 2, 6, 7, 8, 9, 10.
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Step 2.
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Find the intersection of the complement of B and A.
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The intersection of complement of B and A is the set of elements
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which are in both the complement of B and A.
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We look for elements that are in our new list and in set A.
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The only number in both is 1.
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Therefore, the intersection of the complement of B and A is 1.
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Step 3.
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Find the union of that result with set C.
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The union of our result set and set C is the set of elements which are in 1, or C, or both.
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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.
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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.
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Your support really keeps me motivated to create more great videos for you.
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Vocabolario e note di pronuncia per questa lezione
Questo video contiene 121 frasi e 1354 parole da ripetere con lo shadowing. Il parlato dura 11:55. Chi parla mantiene un ritmo costante di circa 114 parole al minuto, comodo per lo shadowing. Solo il 79% delle parole rientra nelle 3.000 più comuni dell’inglese, quindi il lessico è impegnativo.
Vocaboli chiave di questo video
15 parole meno comuni del video, con pronuncia e significato:
- element /ˈɛləmənt/ (sostantivo) — elemento. 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/ (sostantivo) — incrocio. The junction of two (or more) paths, streets, highways, or other thoroughfares.
- complement /ˈkɑmpləmənt/ (sostantivo) — angolo complementare. The totality, the full amount or number which completes something.
- subset /ˈsʌbˌsɛt/ (sostantivo) — sottoinsieme. A set A such that every element of A is also an element of S.
- symbol /ˈsɪmbəl/ (sostantivo) — simbolo. A character or glyph representing an idea, concept or object.
- brace /bɹeɪs/ (sostantivo) — abbraccio. A curved instrument or handle of iron or wood, for holding and turning bits, etc.; a bitstock.
- mathematics /mæθ(.ə)ˈmæt.ɪks/ (sostantivo) — matematica. An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them.
- combine /kəmˈbaɪn/ (verbo) — combinare, mischiare. To bring (two or more things or activities) together; to unite.
- subscribe /səbˈskɹaɪb/ (verbo) — abbonarsi. To write (one’s name) at the bottom of a document; to sign (one's name).
- motivate /ˈmoʊ.tɪ.veɪt/ (verbo) — motivare. To provide someone with an incentive to do something; to encourage; to actuate.
- involve /ɪnˈvɑlv/ (verbo) — coinvolgere. To have (something) as a component or a related part; to comprise, to include.
- dive /daɪv/ (verbo) — immergersi. To swim under water.
- tricky /ˈtɹɪk.i/ (aggettivo) — insidioso, ingannevole. Hard to deal with, complicated.
- bracket /ˈbɹækɪt/ (sostantivo) — staffa. A fixture attached to a wall to hold up a shelf.
- alternatively /ɔlˈtɝ.nə.tɪv.li/ (avverbio) — in alternativa. in an alternative way
I phrasal verb che sentirai
- look at (verbo) — guardare. To observe or watch.
- look for (verbo) — cercare, ricercare. To seek.
Pronuncia a cui fare attenzione
Chi parla usa 8 contrazioni e forme ridotte, come I'd, we're, don't. Pronunciale nella forma breve, così come le senti.
- I suoni “sh” e “zh”: intersection /ˈɪntəɹˌsɛkʃən/, notation /noʊˈteɪʃən/, foundational /faʊnˈdeɪ.ʃə.nəl/
- Parole lunghe — attenzione all’accento: intersection /ˈɪntəɹˌsɛkʃən/, universal /ˌjunəˈvɜɹs(ə)l/, mathematics /mæθ(.ə)ˈmæt.ɪks/, alternatively /ɔlˈtɝ.nə.tɪv.li/, foundational /faʊnˈdeɪ.ʃə.nəl/
Come esercitarsi con questo video
- Ascolta tutto il video una volta senza parlare e annota le parole che non conosci.
- Fai shadowing frase per frase a velocità normale, ripetendo ognuna finché il tuo ritmo coincide con quello di chi parla.
- Registrati e confronta con l’originale, facendo attenzione a parole come element, intersection, complement.
La grammatica di questo video
Le strutture che chi parla usa di più, con le parole esatte del video:
| Struttura | Nel video |
|---|---|
| Frasi condizionali if + frase, will/would + verbo — una condizione e il suo risultato | If it does, I'd super |
| Forma passiva be + participio passato — conta ciò che accade, non chi lo fa | is made · are called · can be described |
| Frasi relative who / which + frase — un’informazione in più su una persona o una cosa | objects, which are · elements which are |
Cos'è la tecnica dello Shadowing?
Shadowing è una tecnica di apprendimento delle lingue supportata da studi scientifici, originariamente sviluppata per la formazione dei traduttori professionisti e resa popolare dal poliglotta Dr. Alexander Arguelles. Il metodo è semplice ma potente: ascolti un audio in inglese di madrelingua e lo ripeti immediatamente ad alta voce — come un'ombra che segue il parlante con un ritardo di solo 1–2 secondi. A differenza dell'ascolto passivo o degli esercizi di grammatica, lo shadowing costringe il tuo cervello e i muscoli della bocca a elaborare e riprodurre simultaneamente i modelli di discorso reale. La ricerca dimostra che migliora significativamente la precisione della pronuncia, l'intonazione, il ritmo, il discorso connesso, la comprensione dell'ascolto e la fluidità del parlato — rendendolo uno dei metodi più efficaci per la preparazione alla prova di speaking dell'IELTS e per la comunicazione reale in inglese.