쉐도잉 연습: SET Notations | Mathematics: IGCSE, GCSE & O Level (CIE/CAIE, Edexcel, AQA, OCR) - 영상으로 영어 말하기 배우기
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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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이 레슨의 어휘와 말하기 포인트
이 영상에는 섀도잉할 문장 121개와 단어 1354개가 있습니다. 말하는 구간의 길이는 11:55입니다. 화자는 분당 약 114단어의 일정한 속도로 말해서 섀도잉하기에 편한 속도입니다. 영어에서 가장 많이 쓰이는 3,000단어에 속하는 단어가 79%뿐이라 어휘가 어려운 편입니다.
이 영상의 핵심 어휘
영상에 나오는 덜 흔한 단어 13개를 발음, 뜻과 함께 정리했습니다.
- element /ˈɛləmənt/ (명사) — 요소. 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/ (명사) — 사거리, 네거리. The junction of two (or more) paths, streets, highways, or other thoroughfares.
- subset /ˈsʌbˌsɛt/ (명사) — 부분집합. A set A such that every element of A is also an element of S.
- symbol /ˈsɪmbəl/ (명사) — 상징, 부호. A character or glyph representing an idea, concept or object.
- universal /ˌjunəˈvɜɹs(ə)l/ (형용사) — 우주(宇宙)의, 우주적. Of or pertaining to the universe.
- mathematics /mæθ(.ə)ˈmæt.ɪks/ (명사) — 수학. An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them.
- combine /kəmˈbaɪn/ (동사) — 조합하다, 결합하다. To bring (two or more things or activities) together; to unite.
- subscribe /səbˈskɹaɪb/ (동사) — 구독하다. To write (one’s name) at the bottom of a document; to sign (one's name).
- motivate /ˈmoʊ.tɪ.veɪt/ (동사) — ...에 동기를 주다. To provide someone with an incentive to do something; to encourage; to actuate.
- dive /daɪv/ (동사) — 잠수하다. To swim under water.
- bracket /ˈbɹækɪt/ (명사) — 괄호. A fixture attached to a wall to hold up a shelf.
- alternatively /ɔlˈtɝ.nə.tɪv.li/ (부사) — 또는. in an alternative way
- integer /ˈɪn.tɪ.d͡ʒə(ɹ)/ (명사) — 정수. A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3, ...}.
영상에 나오는 구동사
- look for (동사) — 찾다, 구하다. To seek.
주의할 발음
화자는 I'd, we're, don't 같은 축약형과 약화된 형태를 8번 사용합니다. 들리는 대로 짧게 발음하세요.
- “sh”와 “zh” 소리: intersection /ˈɪntəɹˌsɛkʃən/, notation /noʊˈteɪʃən/, foundational /faʊnˈdeɪ.ʃə.nəl/
- 긴 단어 — 강세 위치에 주의: intersection /ˈɪntəɹˌsɛkʃən/, universal /ˌjunəˈvɜɹs(ə)l/, mathematics /mæθ(.ə)ˈmæt.ɪks/, alternatively /ɔlˈtɝ.nə.tɪv.li/, foundational /faʊnˈdeɪ.ʃə.nəl/
이 영상으로 연습하는 방법
- 먼저 말하지 않고 영상을 끝까지 듣고 모르는 단어를 적어 둡니다.
- 보통 속도로 한 문장씩 섀도잉하고, 화자의 리듬과 맞을 때까지 반복합니다.
- 자신의 목소리를 녹음해 원본과 비교하고, element, intersection, subset 같은 단어에 특히 주의합니다.
이 영상의 문법
화자가 가장 많이 쓰는 문형을 영상 속 실제 표현과 함께 정리했습니다.
| 문형 | 영상 속 표현 |
|---|---|
| 조건문 if + 절, will/would + 동사 — 조건과 그 결과 | If it does, I'd super |
| 수동태 be + 과거분사 — 누가 하는지보다 무슨 일이 일어나는지에 초점 | is made · are called · can be described |
| 관계절 who / which + 절 — 사람이나 사물에 대한 추가 정보 | objects, which are · elements which are |
쉐도잉이란? 영어 실력을 빠르게 키우는 과학적 방법
쉐도잉(Shadowing)은 원래 전문 통역사 훈련을 위해 개발된 언어 학습 기법으로, 다언어 학자인 Dr. Alexander Arguelles에 의해 대중화된 방법입니다. 핵심 원리는 간단하지만 매우 강력합니다: 원어민의 영어를 들으면서 1~2초의 짧은 지연으로 즉시 소리 내어 따라 말하는 것——마치 '그림자(shadow)'처럼 화자를 따라가는 것입니다. 문법 공부나 수동적인 청취와 달리, 쉐도잉은 뇌와 입 근육이 동시에 실시간으로 영어를 처리하고 재현하도록 훈련합니다. 연구에 따르면 이 방법은 발음 정확도, 억양, 리듬, 연음, 청취력, 말하기 유창성을 크게 향상시킵니다. IELTS 스피킹 준비와 자연스러운 영어 소통을 원하는 분들에게 특히 효과적입니다.