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  • ID: 460605
  • Uploader: redtails »
  • Date: 2009-09-24 17:43
  • Update: 2026-07-25 23:27
  • Size: 885.7 KB .jpg (1600x1200) »
  • Top tagger: redtails (25)
  • Source: i.pximg.net more
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Media asset #1
Cirno's Perfect Math Class
Set - part 1
* A set is a collection of distinct objects. Each object that makes up the set is called an element or member of the set.
Exercise
Exercise
We asked 100 people whether you are "good or bad" at playing Touhou, and whether you have "one wife or more". The survey showed 43 are "good", 29 are "one wife", and 35 are "bad and more wives".
How many people are good and have one wife? Answer is 7.
How many people are good and have one wife? Answer is 7.
How many people are good and have many wives? Answer is 36.
How many people are good and have many wives? Answer is 36.
"a" is a member of set "A".
A is contained in B. (= B contains A.)
"Sets A and B are equal" (It implies "A ⊂ B" and "A ⊃ B")
Intersection
Intersection
The set that contains all elements which are in A as well as in B.
Union
The collection of elements which are in A or in B.
The collection of elements which are in A or in B.
Complement of A
If a "universe set" U is defined, the collection of elements in U, but not in A.
If a "universe set" U is defined, the collection of elements in U, but not in A.
Empty set
The Greek letter "Φ" In fact, this symbol is not related to the Greek letter.
The set having no elements.
The chart below is called a Venn diagram.
The square's interior is a universal set.
The red part is
The yellow part is
The yellow part is
This blue part.
The green part.
The green part.
De Morgan's laws
Let universal set U={integers from 1 to 10 inclusive} have subsets A and B so that A∩B={3,6,8}, A'∩B'={4,5,7}, A∩B'={1,10} Find sets A, B, and A∪B. Ans: A={1,3,6,8,10} B={2,3,6,8,9} A∪B={1,2,3,6,8,9,10}
Cardinality
n(P) indicates the number of elements in a finite set P. For following examples, A and B are finite sets, meaning they only contain finitely many elements.
If we just claculate n(A)+n(B) as the Venn diagram might suggest, the middle section which is the intersection of A and B will be counted twice.
Φ has no element = has 0 elements.
Refer to the graph.
Let U be the universal set of integers from 1 to 1000 inclusive. If subsets A={multiples of 3}, B={multiples of 5}, find n(A'∩B'). Ans:533
Among the integers of 1 to 100 inclusive, find the number of integers in the following.
Is a multiple of both 4 and 7. Ans:3
Neither a multiple of 4 or 7. Ans:64
Is a multiple of 4 but not of 7. Ans: 22
Either a multiple of 4 or 7. Ans:36

Artist's commentary

チルノのパーフェクト数学教室

取りあえず…ネタに悩んだ結果生まれた、受験生応援プロジェクト…その名も「チルノのパーフェクト数学教室」!
毎週一回数学についてチルノ先生に教えてもらおうという話でさらに宿題もあるよという嫌がらせが至れり尽くせり!取りあえず集合の話。

ボケなしの割と本気で書いてみましたが…完全に需要ないと思うので今回で即終了w
需要があれば他のキャラで別科目も…などと夢見つつ…ってかこんなものしか考えれない時点で相当スランプですよね~……まぁ眼鏡チルノが描きたかったということでここは一つ(´・ω・`)
■一応追加修正で…ベン図でA∪Bは黄色の部分と書いてますが、正しくは黄色+赤色です、すいません。

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    Cirno's Perfect Math Class
    Set - part 1
    * A set is a collection of distinct objects. Each object that makes up the set is called an element or member of the set.
    Exercise
    Exercise
    We asked 100 people whether you are "good or bad" at playing Touhou, and whether you have "one wife or more". The survey showed 43 are "good", 29 are "one wife", and 35 are "bad and more wives".
    How many people are good and have one wife? Answer is 7.
    How many people are good and have one wife? Answer is 7.
    How many people are good and have many wives? Answer is 36.
    How many people are good and have many wives? Answer is 36.
    "a" is a member of set "A".
    A is contained in B. (= B contains A.)
    "Sets A and B are equal" (It implies "A ⊂ B" and "A ⊃ B")
    Intersection
    Intersection
    The set that contains all elements which are in A as well as in B.
    Union
    The collection of elements which are in A or in B.
    The collection of elements which are in A or in B.
    Complement of A
    If a "universe set" U is defined, the collection of elements in U, but not in A.
    If a "universe set" U is defined, the collection of elements in U, but not in A.
    Empty set
    The Greek letter "Φ" In fact, this symbol is not related to the Greek letter.
    The set having no elements.
    The chart below is called a Venn diagram.
    The square's interior is a universal set.
    The red part is
    The yellow part is
    The yellow part is
    This blue part.
    The green part.
    The green part.
    De Morgan's laws
    Let universal set U={integers from 1 to 10 inclusive} have subsets A and B so that A∩B={3,6,8}, A'∩B'={4,5,7}, A∩B'={1,10} Find sets A, B, and A∪B. Ans: A={1,3,6,8,10} B={2,3,6,8,9} A∪B={1,2,3,6,8,9,10}
    Cardinality
    n(P) indicates the number of elements in a finite set P. For following examples, A and B are finite sets, meaning they only contain finitely many elements.
    If we just claculate n(A)+n(B) as the Venn diagram might suggest, the middle section which is the intersection of A and B will be counted twice.
    Φ has no element = has 0 elements.
    Refer to the graph.
    Let U be the universal set of integers from 1 to 1000 inclusive. If subsets A={multiples of 3}, B={multiples of 5}, find n(A'∩B'). Ans:533
    Among the integers of 1 to 100 inclusive, find the number of integers in the following.
    Is a multiple of both 4 and 7. Ans:3
    Neither a multiple of 4 or 7. Ans:64
    Is a multiple of 4 but not of 7. Ans: 22
    Either a multiple of 4 or 7. Ans:36

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