शैडोइंग अभ्यास: SET Notations | Mathematics: IGCSE, GCSE & O Level (CIE/CAIE, Edexcel, AQA, OCR) - वीडियो के साथ अंग्रेजी बोलना सीखें

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Welcome to Plaid Academy.

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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.

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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.

103

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,

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.

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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.

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.

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Your support really keeps me motivated to create more great videos for you.

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अनुशंसित वीडियो

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इस वीडियो में शैडोइंग के लिए 121 वाक्य और 1354 शब्द हैं। बोला गया हिस्सा 11:55 लंबा है। वक्ता लगभग 114 शब्द प्रति मिनट की स्थिर गति से बोलता है, जो शैडोइंग के लिए आरामदायक है। केवल 79% शब्द अंग्रेज़ी के 3,000 सबसे आम शब्दों में से हैं, इसलिए शब्दावली कठिन है।

इस वीडियो की मुख्य शब्दावली

वीडियो के 10 कम प्रचलित शब्द, उच्चारण और अर्थ के साथ:

element /ˈɛləmənt/ (संज्ञा) — तत्त्व. 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/ (संज्ञा) — चौराहा, दोराहा. The junction of two (or more) paths, streets, highways, or other thoroughfares.
subset /ˈsʌbˌsɛt/ (संज्ञा) — उपसमुच्चय. A set A such that every element of A is also an element of S.
symbol /ˈsɪmbəl/ (संज्ञा) — प्रतीक, चिह्न. A character or glyph representing an idea, concept or object.
mathematics /mæθ(.ə)ˈmæt.ɪks/ (संज्ञा) — गणित, गणित-विधा. An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them.
combine /kəmˈbaɪn/ (क्रिया) — मिलाना. To bring (two or more things or activities) together; to unite.
motivate /ˈmoʊ.tɪ.veɪt/ (क्रिया) — प्रेरित करना. To provide someone with an incentive to do something; to encourage; to actuate.
dive /daɪv/ (क्रिया) — डुबकी. To swim under water.
bracket /ˈbɹækɪt/ (संज्ञा) — कोष्ठक. A fixture attached to a wall to hold up a shelf.
integer /ˈɪn.tɪ.d͡ʒə(ɹ)/ (संज्ञा) — पूर्णांक, पूर्ण संख्या. A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3, ...}.

वीडियो में आने वाली फ़्रेज़ल वर्ब

look at (क्रिया) — हेरना. To observe or watch.
look for (क्रिया) — ढूँढ़ना, ढूँढना. To seek.

ध्यान देने योग्य उच्चारण

वक्ता 8 बार संक्षिप्त रूपों का प्रयोग करता है, जैसे I'd, we're, don't। इन्हें वैसे ही छोटा बोलें जैसा आप सुनते हैं।

“sh” और “zh” की ध्वनियाँ: intersection /ˈɪntəɹˌsɛkʃən/, notation /noʊˈteɪʃən/, foundational /faʊnˈdeɪ.ʃə.nəl/
लंबे शब्द — बलाघात सही रखें: intersection /ˈɪntəɹˌsɛkʃən/, universal /ˌjunəˈvɜɹs(ə)l/, mathematics /mæθ(.ə)ˈmæt.ɪks/, alternatively /ɔlˈtɝ.nə.tɪv.li/, foundational /faʊnˈdeɪ.ʃə.nəl/

इस वीडियो से अभ्यास कैसे करें

पहले बिना बोले पूरा वीडियो एक बार सुनें और जो शब्द नहीं आते उन्हें लिख लें।
सामान्य गति पर एक-एक वाक्य की शैडोइंग करें और हर वाक्य तब तक दोहराएँ जब तक आपकी लय वक्ता से न मिल जाए।
अपनी आवाज़ रिकॉर्ड करें और मूल से तुलना करें, ख़ासकर element, intersection, subset जैसे शब्दों पर ध्यान दें।

इस वीडियो का व्याकरण

वक्ता जिन संरचनाओं का सबसे अधिक प्रयोग करता है, वीडियो के असली शब्दों के साथ:

संरचना	वीडियो में
शर्त वाले वाक्य if + उपवाक्य, will/would + क्रिया — शर्त और उसका नतीजा	If it does, I'd super
Passive voice be + past participle — ज़ोर इस पर कि क्या होता है, न कि कौन करता है	is made · are called · can be described
Relative clauses who / which + उपवाक्य — व्यक्ति या वस्तु के बारे में अतिरिक्त जानकारी	objects, which are · elements which are

शैडोइंग तकनीक क्या है?

शैडोइंग (Shadowing) एक विज्ञान-समर्थित भाषा सीखने की तकनीक है जो मूल रूप से पेशेवर दुभाषिया प्रशिक्षण के लिए विकसित की गई थी। विधि सरल लेकिन शक्तिशाली है: आप मूल अंग्रेज़ी ऑडियो सुनते हैं और तुरंत इसे ज़ोर से दोहराते हैं — जैसे वक्ता की छाया 1-2 सेकंड की देरी से। शोध से पता चलता है कि यह उच्चारण सटीकता, स्वर, लय, जुड़ी हुई ध्वनियाँ, सुनने की समझ और बोलने की प्रवाहशीलता में काफ़ी सुधार करता है।

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शैडोइंग अभ्यास: SET Notations | Mathematics: IGCSE, GCSE & O Level (CIE/CAIE, Edexcel, AQA, OCR) - वीडियो के साथ अंग्रेजी बोलना सीखें

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