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!
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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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Vocabulario y notas de pronunciación para esta lección
Este vídeo tiene 121 frases y 1354 palabras para practicar shadowing. La parte hablada dura 11:55. El hablante mantiene un ritmo constante de unas 114 palabras por minuto, cómodo para el shadowing. Solo el 79 % de las palabras está entre las 3.000 más comunes del inglés, por lo que el vocabulario es exigente.
Vocabulario clave de este vídeo
15 palabras menos comunes del vídeo, con su pronunciación y significado:
- element /ˈɛləmənt/ (sustantivo) — 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/ (sustantivo) — cruce. The junction of two (or more) paths, streets, highways, or other thoroughfares.
- subset /ˈsʌbˌsɛt/ (sustantivo) — subconjunto. A set A such that every element of A is also an element of S.
- symbol /ˈsɪmbəl/ (sustantivo) — símbolo. A character or glyph representing an idea, concept or object.
- universal /ˌjunəˈvɜɹs(ə)l/ (adjetivo) — universal. Of or pertaining to the universe.
- brace /bɹeɪs/ (sustantivo) — abrazadera. A curved instrument or handle of iron or wood, for holding and turning bits, etc.; a bitstock.
- mathematics /mæθ(.ə)ˈmæt.ɪks/ (sustantivo) — matemáticas, matemática. An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them.
- combine /kəmˈbaɪn/ (verbo) — combinar, juntar. To bring (two or more things or activities) together; to unite.
- subscribe /səbˈskɹaɪb/ (verbo) — suscribirse, subscribirse. To write (one’s name) at the bottom of a document; to sign (one's name).
- motivate /ˈmoʊ.tɪ.veɪt/ (verbo) — motivar. To provide someone with an incentive to do something; to encourage; to actuate.
- involve /ɪnˈvɑlv/ (verbo) — involucrar. To have (something) as a component or a related part; to comprise, to include.
- dive /daɪv/ (verbo) — bucear, somorgujar. To swim under water.
- tricky /ˈtɹɪk.i/ (adjetivo) — dificultoso, chungo. Hard to deal with, complicated.
- bracket /ˈbɹækɪt/ (sustantivo) — consola, soporte. A fixture attached to a wall to hold up a shelf.
- alternatively /ɔlˈtɝ.nə.tɪv.li/ (adverbio) — si no, en lugar de. in an alternative way
Phrasal verbs que vas a escuchar
- talk about (verbo) — hablar de, hablar sobre. Used to draw attention to the speaker's characterization of someone or something.
- look at (verbo) — mirar, funar. To observe or watch.
- look for (verbo) — buscar, lambisquear. To seek.
Pronunciación a tener en cuenta
El hablante usa 8 contracciones y formas reducidas, como I'd, we're, don't. Dilas en su forma corta, tal como las oyes.
- Los sonidos de “sh” y “zh”: intersection /ˈɪntəɹˌsɛkʃən/, notation /noʊˈteɪʃən/, foundational /faʊnˈdeɪ.ʃə.nəl/
- Palabras largas — cuida el acento: intersection /ˈɪntəɹˌsɛkʃən/, universal /ˌjunəˈvɜɹs(ə)l/, mathematics /mæθ(.ə)ˈmæt.ɪks/, alternatively /ɔlˈtɝ.nə.tɪv.li/, foundational /faʊnˈdeɪ.ʃə.nəl/
Cómo practicar con este vídeo
- Escucha el vídeo entero una vez sin hablar y anota las palabras que no conoces.
- Haz shadowing frase por frase a velocidad normal, repitiendo cada una hasta que tu ritmo coincida con el del hablante.
- Grábate y compara con el original, prestando atención a palabras como element, intersection, subset.
Gramática en este vídeo
Las estructuras que más usa el hablante, con las palabras exactas del vídeo:
| Estructura | En el vídeo |
|---|---|
| Oraciones condicionales if + oración, will/would + verbo — una condición y su resultado | If it does, I'd super |
| Voz pasiva be + participio pasado — importa lo que ocurre, no quién lo hace | is made · are called · can be described |
| Oraciones de relativo who / which + oración — información extra sobre una persona o cosa | objects, which are · elements which are |
¿Qué es la Técnica de Shadowing?
Shadowing es una técnica de aprendizaje de idiomas respaldada por la ciencia, desarrollada originalmente para la formación de intérpretes profesionales y popularizada por el políglota Dr. Alexander Arguelles. El método es simple pero poderoso: escuchas audio en inglés nativo y lo repites en voz alta de inmediato, como una sombra que sigue al hablante con solo 1-2 segundos de retraso. A diferencia de la escucha pasiva o los ejercicios de gramática, el shadowing obliga a tu cerebro y músculos de la boca a procesar y reproducir simultáneamente patrones de habla reales. Las investigaciones muestran que mejora significativamente la precisión de la pronunciación, la entonación, el ritmo, el habla conectada, la comprensión auditiva y la fluidez al hablar, convirtiéndola en una de las metodologías más efectivas para la preparación del IELTS Speaking y la comunicación en inglés en el mundo real.