2. Himpunan

Himpunan - @acoxstpd
a. 𝐴 ∩ (𝐵 ∪ 𝐶)
Quiz Kuantitatif #2: Himpunan
b. 𝐴 ∪ (𝐵 ∩ 𝐶)
Key points:
c. (𝐴 ∪ 𝐵) − 𝐶
d. (𝐴 ∩ 𝐵) − 𝐶
a. Memahami operasi ∩ , ∪ ,
komplemen, dan – pada himpunan.
e. 𝐴 − (𝐵 ∩ 𝐶)
2. [JEE
MAIN
SAMPLE
PAPER] What does the shaded
portion of the Venn diagram given
below represent?
b. Dapat menentukan daerah dari
operasi (a).
c. Mengerti akan notasi ⊂ dan ⊆
pada dua buah himpunan.
d. Mengerti konsep bahwa 𝑛(𝐴 ∪
𝐵) = 𝑛(𝐴) + 𝑛(𝐵) − 𝑛(𝐴 ∩ 𝐵).
e. Mengerti konsep untuk menentukan
jumlah pemetaan yang mungkin
dan konsep korespondensi satusatu.
f.
Nilai maksimum dan minimum dari
sebuah irisan diagram Venn.
a. (𝑃 ∩ 𝑄) ∩ (𝑃 ∩ 𝑅)
g. Vocabulary:
shaded
region,
elements, number of elements,
number of distinct functions,
number of bijections, maximum and
minimum percentage, greatest and
lowest number, respectively.
b.
(𝑃 ∩ 𝑄) − 𝑅 ∪ ((𝑃 ∩ 𝑅) − 𝑄)
c.
(𝑃 ∪ 𝑄) − 𝑅 ∩ ((𝑃 ∩ 𝑅) − 𝑄)
d.
(𝑃 ∩ 𝑄) ∪ 𝑅 ∩ ((𝑃 ∪ 𝑄) − 𝑅)
e. None of the above
3. [JEE
MAIN
SAMPLE
PAPER] What does the shaded
portion of the Venn diagram given
below represent?
h. Catatan: Untuk variasi soal
yang lebih banyak, silahkan
cek bit.ly/KitabNumerik Bab
XVIII: Himpunan
1. [UTBK 2019] Daerah yang diarsir
menyatakan himpunan …
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Himpunan - @acoxstpd
a. 𝐶 ∩ (𝐴 ∩ 𝐵 )
(i)
𝐶 −𝐵
b. 𝐶 ∪ (𝐶 ∩ 𝐴 ∩ 𝐵)
(ii)
(𝐷 ∩ 𝐵 ) − 𝐴
c. 𝐶 ∪ (𝐶 ∩ 𝐴) ∪ (𝐶 ∩ 𝐵)
(iii)
𝐶 − (𝐵 ∪ 𝐷)
d. 𝐶 ∪ (𝐴 − 𝐵)
(iv)
𝐵 ∩𝐴 ∩𝐷
e. None of the above
a. (i), (ii), and (iii)
b. (i) and (iii)
4. [SOAL PENULIS] What does
the shaded portion of the Venn
diagram given below represent?
c. (ii) and (iv)
d. (iv) only
e. (i), (ii), (iii), and (iv)
6. [MODIFIKASI SOAL NF]
Diberikan dua himpunan A dan B.
Himpunan A memiliki anggota
sebanyak 10 anggota dan himpunan
B memiliki anggota sebanyak 5
anggota. Berapa jumlah anggota
dari himpunan 𝐴 ∪ 𝐵?
(1)
𝐵⊂𝐴
a. (𝐴 ∩ 𝐵 ∩ 𝐷) ∩ (𝐶 ∩ 𝐴 ∩ 𝐷)
(2)
𝑛(𝐴 ∩ 𝐵) = 5
b. (𝐴 ∩ 𝐵 ∩ 𝐷 ∩ 𝐶)
a. Pernyataan (1) SAJA cukup
untuk menjawab pertanyaan,
tetapi pernyataan (2) SAJA
tidak cukup.
c.
(𝐴 ∩ 𝐵 ∩ 𝐷) − 𝐶 ∪ ((𝐴 ∩ 𝐶 ∩
𝐷) − 𝐵)
d. (𝐴 ∪ 𝐵) − (𝐵 ∪ 𝐶) − (𝐶 ∪ 𝐷)
b. Pernyataan (2) SAJA cukup
untuk menjawab pertanyaan,
tetapi pernyataan (1) SAJA
tidak cukup.
e. 𝐴 ∪ 𝐵 ∪ 𝐶 ∪ 𝐷
5. [SOAL PENULIS] What does
the shaded portion of the Venn
diagram given below represent?
c. DUA pernyataan BERSAMASAMA cukup untuk menjawab
pertanyaan,
tetapi
SATU
pernyataan SAJA tidak cukup.
d. Pernyataan (1) SAJA cukup
untuk menjawab pertanyaan
dan pernyataan (2) SAJA
cukup.
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Himpunan - @acoxstpd
e. Pernyataan (1) dan pernyataan
(2)
tidak
cukup
untuk
menjawab pertanyaan.
c. 𝑃 = 𝑄
d. There is not enough information
included to determine the
relationship.
7. [SOAL PENULIS] You are given
a Venn diagram with its elements as
shown below:
9. [SOAL PRIBADI] Given sets
𝐴, 𝐵, 𝐶, 𝐷 where
𝑛(𝐴) = 𝑛(𝐵) = 4, 𝑛(𝐶) = 5, and
𝑛(𝐷) = 6,
examine
the
relationship between 𝑃 and 𝑄
given their definitions below.
If 𝑛(𝐴) gives you the number of
elements contained in set 𝐴 , the
value of 𝑛 (𝐶 − 𝐴) ∪ (𝐴 ∩ 𝐶) is
…
a. 1
𝑃
𝑄
The number
of bijections
that can be
made from set
𝐴 to set 𝐵.
The number
of bijections
that can be
made from set
𝐶 to set 𝐷.
a. 𝑃 > 𝑄
b. 3
b. 𝑄 > 𝑃
c. 5
c. 𝑃 = 𝑄
d. 6
d. There
is
not
enough
information
included
to
determine the relationship.
e. 8
8. [SOAL PRIBADI] Given 𝐴 =
{1, 2, 3} and 𝐵 = {4, 5} , examine
the relationship between 𝑃 and 𝑄
given their definitions below.
𝑃
10. [UN SMP] Himpunan pasangan
berurutan berikut yang merupakan
pemetaan satu-satu adalah …
a. {(𝑎, 0), (𝑎, 2), (𝑏, 1), (𝑐, 1)}
𝑄
b. {(𝑎, 0), (𝑎, 2), (𝑏, 1), (𝑏, 3)}
The number of The number of
distinct
distinct
functions
functions
𝑓: [𝐴] → [𝐵] in 𝑓: [𝐵] → [𝐴] in
total.
total.
c. {(𝑎, 1), (𝑎, 3), (𝑎, 5), (𝑐, 7)}
d. {(𝑎, 1), (𝑐, 3), (𝑑, 2), (𝑓, 3)}
e. {(𝑎, 1), (𝑐, 3), (𝑑, 2), (𝑓, 4)}
11. [GMAT, VERITAS PREP,
EDITED] In an exam, it is found
that 80% people solved question A
a. 𝑃 > 𝑄
b. 𝑄 > 𝑃
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Himpunan - @acoxstpd
and 75% people solved question B.
What is the maximum and
minimum percentage of people who
could have solved both questions,
respectively?
a. 75%, 55%
b. 55%, 75%
c. 75%, 60%
d. 65%, 60%
e. 80%, 55%
12. [GMAT] In a village of 100
households, 75 have at least one
DVD player, 80 have at least one
cell phone, and 55 have at least one
MP3 player. If 𝑥 and 𝑦 are
respectively the greatest and lowest
possible number of households that
have all three of these devices, 𝑥 −
𝑦 is …
a. 65
b. 55
c. 45
d. 35
e. 25
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