Yaadannoo boqonnaa fi gaaffii shaakalaa

Boqonnaa 1 Herrega kutaa 9: Dabalata Waa'ee Tuutaalee

Wanti fuula kana irra jiru hundi boqonnaa 1 kitaaba Herrega kutaa 9 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.

3
Kaardii: 10
Gaaffii shaakalaa boqonnaa 1: 1–16
Fuula kitaabaa boqonnaa 1

Boqonnaan 1 maal haguuga

1.Description of the Concept Set
2.Notion of Set
3.Operations on Sets
4.Application of Operations on Sets

Yaadannoo gabaabaa boqonnaa 1

Kaardiiwwan fuula Herrega kutaa 9 irratti boqonnaa kana jala galmaa'an. Tokko tokkoon bani.

Foormulaa lakkoofsa tuutaaGabatee wabiiTwo sets · Complement · In A only · +4

Seera	Foormulaa
Two sets	$n(A \cup B) = n(A) + n(B) - n(A \cap B)$
Complement	$n(A') = n(U) - n(A)$
In $A$ only	$n(A) - n(A \cap B)$
Three sets	$n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(A \cap C) - n(B \cap C) + n(A \cap B \cap C)$
Disjoint sets	$n(A \cup B) = n(A) + n(B)$
De Morgan	$(A \cup B)' = A' \cap B'$
De Morgan	$(A \cap B)' = A' \cup B'$
Subsets of a set	$2^{n}$ for a set of $n$ members

Yoom akka itti fayyadamtu

Yeroo gaaffiin namoota yookaan wantoota al tokkotti garee tokkoo ol keessa jiran lakkaa'u isaan kana fayyadami; gaaffiin fakkii Veen hundi dhugumatti isuma. Fakkicha kaasi; duraan dursii kutaa gidduu guuti; ergasii gara alaatti deemi.

Of eeggadhu

Tuuta sadiin mallattoon wal jijjiira: cimdii tokkoon tokkoon hir'isi; ergasii walgahiinsa sadeenii deebisii ida'i. Kutaa dhumaa sana dhiisuun karaa guddaa gaaffiin Veen geengoo sadii itti dogoggorudha; sababiin isaas kutaan gidduu al tokko utuu hin taane al zeeroo lakkaa'ama.

Baay'ina Miseensota Tokkummaa Tuutota LamaaFoormulaa

n(A \cup B) = n(A) + n(B) - n(A \cap B)

n(A \cup B) = n(A) + n(B) - n(A \cap B)

$n(A \cup B)$: baay'ina miseensota tokkummaa A fi B $1$
$n(A)$: baay'ina miseensota tuuta A $1$
$n(B)$: baay'ina miseensota tuuta B $1$
$n(A \cap B)$: baay'ina miseensota walqaxxaamura A fi B $1$

Yoom akka itti fayyadamtu

Gaaffilee jechootaa fi lakkoofsa miseensota tuutota wal keessa jiran shallaguuf itti fayyadami.

Of eeggadhu

Walqaxxaamura isaanii n(A and B) hir'isuu hin dagatin, yoo hin taane miseensonni waliinii al lama lakkaa'amu.

Grade 9 Mathematics, fuula 1-86 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Gabatee Baay'ina Tuuta-xiqqaa fi Tuuta-xiqqaa SirriiGabatee wabiiAll Subsets · Proper Subsets

Gosa Tuutaa	Foormulaa Miseensa n Qabuuf	Fakkeenya n = 3 Ta'eef
All Subsets	$2^n$	$2^3 = 8$
Proper Subsets	$2^n - 1$	$2^3 - 1 = 7$

Yoom akka itti fayyadamtu

Tuuta dhuma qabu tokko irraa tuutota-xiqqaa meeqa uumuun akka danda'amu shallaguuf gargaara.

Of eeggadhu

Tuunni kamiyyuu ofiisaatiif tuuta-xiqqaa sirrii ta'uu hin danda'u, kanaaf lakkoofsa isaanii irraa 1 hir'ifama.

Grade 9 Mathematics, fuula 1-86 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Gaaffii shaakalaa boqonnaa 1

Gaaffii filannoo 10 boqonnaa kana irratti barreeffaman, tokkoon tokkoon isaanii deebii fi sababa qabu. Deebii banuu dura yaali. Gaaffiin kun Ingiliffaa tiin.

Gaaffii 1

Which of these is a well-defined set?

A.The beautiful girls in your class
B.The hardworking teachers in a school
C.The natural numbers less than 100
D.The handsome boys in your school

Deebii fi sababa agarsiisi

Deebii: C The natural numbers less than 100

Sababa

A set is well-defined when, for any object, we can tell whether it is in the set or not. The natural numbers less than 100 can be listed exactly, so we can always decide if a number belongs. Words like beautiful, hardworking and handsome are opinions, so those collections are not well-defined.

Gaaffii 2

Let A = {1, 2, 3, 4, 5, 6}. Which symbol goes in the blank?
8 ____ A

A.∈
B.∉
C.⊆
D.⊂

Deebii fi sababa agarsiisi

Deebii: B ∉

Sababa

The symbol ∈ means belongs to, and ∉ means does not belong to. The number 8 is not in the list {1, 2, 3, 4, 5, 6}, so we write 8 ∉ A.

Gaaffii 3

The set of days in a week is a ______ set.

A.finite
B.infinite
C.empty
D.equivalent

Deebii fi sababa agarsiisi

Deebii: A finite

Sababa

A finite set has a definite, limited number of elements. A week has exactly 7 days, so the set of days in a week is finite.

Gaaffii 4

Let A = {1, 2, 3, ..., 10}. Find n(A), the number of elements of A.

A.9
B.10
C.11
D.100

Deebii fi sababa agarsiisi

Deebii: B 10

Sababa

The set A has the numbers 1 up to 10. Counting them gives 10 elements, so n(A) = 10.

Gaaffii 5

Which set is described by the set builder form {x : x ∈ ℕ and x < 11}?

A.{0, 1, 2, ..., 10}
B.{2, 4, 6, 8, 10}
C.{1, 2, 3, ..., 10}
D.{1, 2, 3, ..., 11}

Deebii fi sababa agarsiisi

Deebii: C {1, 2, 3, ..., 10}

Sababa

Read the rule as: x is a natural number and x is less than 11. Natural numbers start at 1, so the values are 1 to 10. Zero is not a natural number, and 11 is not less than 11.

Gaaffii 6

Let A = {1, 2, 3}. How many proper subsets does A have?

Deebii fi sababa agarsiisi

Deebii: D 7

Sababa

A finite set with n elements has 2ⁿ subsets, and 2ⁿ − 1 proper subsets. Here n = 3, so there are 2³ − 1 = 8 − 1 = 7 proper subsets. The list is {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3} and the empty set.

Gaaffii 7

Let A = {1, 2, 3, 4} and B = {Red, Blue, Green, Black}. Which statement is true?

A.A and B are equal sets.
B.A is a proper subset of B.
C.A and B are equivalent sets.
D.A is an infinite set.

Deebii fi sababa agarsiisi

Deebii: C A and B are equivalent sets.

Sababa

Two finite sets are equivalent when they have the same number of elements. Both A and B have 4 elements, so they are equivalent. They are not equal, because equal sets must have exactly the same elements, and these two sets have different elements.

Gaaffii 8

Let A = {0, 1, 3, 5, 7} and B = {1, 2, 3, 4, 6, 7}. Find A ∩ B.

A.{1, 3, 7}
B.{0, 5}
C.{2, 4, 6}
D.{1, 2, 3, 4, 5, 6, 7}

Deebii fi sababa agarsiisi

Deebii: A {1, 3, 7}

Sababa

The intersection A ∩ B is the set of elements that are in both A and B. The numbers 1, 3 and 7 appear in both sets, so A ∩ B = {1, 3, 7}.

Gaaffii 9

Let A = {1, 2, 4, 5, 8} and B = {2, 3, 5, 7}. Find the symmetric difference A ∆ B.

A.{2, 5}
B.{1, 4, 8}
C.{1, 3, 4, 7, 8}
D.{1, 2, 3, 4, 5, 7, 8}

Deebii fi sababa agarsiisi

Deebii: C {1, 3, 4, 7, 8}

Sababa

First find A \ B, the elements in A but not in B: {1, 4, 8}. Then find B \ A, the elements in B but not in A: {3, 7}. The symmetric difference is the union of these two sets, so A ∆ B = {1, 4, 8} ∪ {3, 7} = {1, 3, 4, 7, 8}.

Gaaffii 10

Let A = {2, 4, 6} and B = {1, 3}. Which ordered pair is an element of B × A?

A.(2, 1)
B.(1, 2)
C.(6, 6)
D.(3, 3)

Deebii fi sababa agarsiisi

Deebii: B (1, 2)

Sababa

In B × A, the first number comes from B and the second number comes from A. B × A = {(1, 2), (1, 4), (1, 6), (3, 2), (3, 4), (3, 6)}. The pair (1, 2) is in this list. The pair (2, 1) belongs to A × B, not B × A.

Appiin boqonnaa kana irratti gaaffii 14 qaba; utuu hojjettuu ni sirreessa. Kan asii jiran 10 jalqabaa ti.

Fuula kitaabaa boqonnaa 1

Boqonnaan 1 Maxxansa Ministeera Barnootaa keessatti fuula 1 hanga fuula 16 ti.

Maxxansa Ministeera Barnootaa, Ingiliffaa, Fuula 337

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Yaadannoo gabaabaa Herrega kutaa 9 hunda

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