Latihan Soal Matematika : Himpunan

1. Jika A = {a,b,c} dan B = {a,b,c,d,e}, maka pernyataan yang salah adalah ...

A B = {a,b,c}

A B = {a,b,c,d,e}

n(A) = 4

B - A = {d,e}

The given statement "n(A) = 4" is incorrect because the cardinality of set A is actually 3, not 4. The set A contains the elements a, b, and c, so the number of elements in set A is 3.

Explanation

The given statement "n(A) = 4" is incorrect because the cardinality of set A is actually 3, not 4. The set A contains the elements a, b, and c, so the number of elements in set A is 3.

2. Manakah diantara himpunan berikut yang merupakan himpunan berhingga?

S = {0,1,2,3,...}

P = {1,2,3, ... ,110}

Q = { ...,-3,-2,-1,0}

R = {...,-3,-2,-1,0,1,...}

The set P = {1,2,3, ... ,110} is a finite set because it contains a specific number of elements, which are the numbers from 1 to 110. The other sets S, Q, and R are all infinite sets because they either include all natural numbers (set S), all negative and non-negative integers (set Q), or all integers (set R), which means they have an infinite number of elements. Therefore, the correct answer is P = {1,2,3, ... ,110} because it is the only set that is finite.

Explanation

The set P = {1,2,3, ... ,110} is a finite set because it contains a specific number of elements, which are the numbers from 1 to 110. The other sets S, Q, and R are all infinite sets because they either include all natural numbers (set S), all negative and non-negative integers (set Q), or all integers (set R), which means they have an infinite number of elements. Therefore, the correct answer is P = {1,2,3, ... ,110} because it is the only set that is finite.

3. Sekelompok siswa terdiri dari 50 orang, setelah di data ternyata 20 orang suka bermain basket, 33 orang suka bermain futsal, dan 5 orang tidak suka bermain kedua-duanya. Banyaknya siswa yang suka bermain basket dan futsal sekaligus adalah ... orang

45

25

15

8

Dari data yang diberikan, terdapat 20 orang yang suka bermain basket dan 33 orang yang suka bermain futsal. Namun, 5 orang di antara mereka tidak suka bermain kedua-duanya. Oleh karena itu, banyaknya siswa yang suka bermain basket dan futsal sekaligus adalah 20 + 33 - 5 = 48.

Explanation

Dari data yang diberikan, terdapat 20 orang yang suka bermain basket dan 33 orang yang suka bermain futsal. Namun, 5 orang di antara mereka tidak suka bermain kedua-duanya. Oleh karena itu, banyaknya siswa yang suka bermain basket dan futsal sekaligus adalah 20 + 33 - 5 = 48.

4. Dalam satu RT terdiri dari 60 warga, 20 warga berlangganan majalah, 35 warga berlangganan koran dan 5 warga berlangganan keduanya. Berapa orang warga yang tidak berlangganan kedua-duanya?

15 warga

30 warga

55 warga

10 warga

There are 20 residents who subscribe to magazines, 35 residents who subscribe to newspapers, and 5 residents who subscribe to both. To find the number of residents who do not subscribe to both, we subtract the number of residents who subscribe to both from the total number of residents who subscribe to either magazines or newspapers. Therefore, the number of residents who do not subscribe to both is 20 + 35 - 5 = 50. Therefore, the correct answer is 10 residents.

Explanation

There are 20 residents who subscribe to magazines, 35 residents who subscribe to newspapers, and 5 residents who subscribe to both. To find the number of residents who do not subscribe to both, we subtract the number of residents who subscribe to both from the total number of residents who subscribe to either magazines or newspapers. Therefore, the number of residents who do not subscribe to both is 20 + 35 - 5 = 50. Therefore, the correct answer is 10 residents.

5.

Perhatikan diagram venn diatas, anggota dari

adalah...

{1,2,3,4,5,7,8,10]

{3,6}

{1,2,3,4,5,6,9,12}

{7,8,10,11}

The correct answer is {1,2,3,4,5,6,9,12} because it is the only set that includes elements from all the other sets in the Venn diagram.

Explanation

The correct answer is {1,2,3,4,5,6,9,12} because it is the only set that includes elements from all the other sets in the Venn diagram.

6. Manakah diantara pernyataan berikut yang merupakan penyajian himpunan dengan cara mendaftar?

B = {himpunan nama bulan yang diawali huruf J}

B = himpunan nama bulan yang diawali dengan huruf J

B = {Januari, Juni, Juli}

B = {x|x diawali huruf J, x nama-nama bulan}

The correct answer is B = {Januari, Juni, Juli}. This is the correct way of representing a set by listing its elements. The set B is defined as the set of month names that start with the letter J, and the elements of this set are explicitly listed as Januari, Juni, and Juli.

Explanation

The correct answer is B = {Januari, Juni, Juli}. This is the correct way of representing a set by listing its elements. The set B is defined as the set of month names that start with the letter J, and the elements of this set are explicitly listed as Januari, Juni, and Juli.

7. Diketahui A = {2,3,5,7} dan B = {1,2,3,4,5} Anggota dari A - B adalah ...

{7}

{1,4}

{1,2,3,4,5}

{2,3,5,7}

The answer {7} is correct because to find the set difference A - B, we need to remove all the elements from set B that are also present in set A. In this case, the only element in set A that is not in set B is 7. Therefore, the set difference A - B is {7}.

Explanation

The answer {7} is correct because to find the set difference A - B, we need to remove all the elements from set B that are also present in set A. In this case, the only element in set A that is not in set B is 7. Therefore, the set difference A - B is {7}.

8. Jika P={bilangan prima kurang dari 18} dan Q={bilangan ganjil antara 3 dan 13}, maka semua anggota himpunan

adalah ...

{5,7,11}

{5,7,13}

{3,5,7,11}

{5,7,11,13}

The set P represents prime numbers less than 18, and the set Q represents odd numbers between 3 and 13. The question asks for the set that contains all the elements of both sets P and Q. Looking at the options, the set {5,7,11} is the only set that contains all the elements of both sets P and Q. Therefore, the correct answer is {5,7,11}.

Explanation

The set P represents prime numbers less than 18, and the set Q represents odd numbers between 3 and 13. The question asks for the set that contains all the elements of both sets P and Q. Looking at the options, the set {5,7,11} is the only set that contains all the elements of both sets P and Q. Therefore, the correct answer is {5,7,11}.

9. Diketahui himpunan A adalah himpunan alat tulis menulis yang dimiliki siswa. Manakah diantara pernyataan berikut ini yang salah?

pensil A

bola basket A

penghapus A

buku tulis A

The given statement that is incorrect is "buku tulis A." This is because "buku tulis" is not a writing tool, but a type of notebook or exercise book. The other options, "pensil A," "bola basket A," and "penghapus A," are all writing tools that can be included in the set A.

Explanation

The given statement that is incorrect is "buku tulis A." This is because "buku tulis" is not a writing tool, but a type of notebook or exercise book. The other options, "pensil A," "bola basket A," and "penghapus A," are all writing tools that can be included in the set A.

10. Diketahui A = {1,2,3,4,5}, B = { 2,4,6,8}, dan S = {1,2,3,4, ... , 10} Anggota dari

adalah ...

{1,2,3,4,5,6,8}

{7,9,10}

{2,4}

{9,10}

The answer {7,9,10} is correct because S is defined as the set of numbers from 1 to 10. However, the numbers 1, 2, 3, 4, 5, 6, and 8 are already included in set A. Therefore, the remaining numbers that are in S but not in A are 7, 9, and 10.

Explanation

The answer {7,9,10} is correct because S is defined as the set of numbers from 1 to 10. However, the numbers 1, 2, 3, 4, 5, 6, and 8 are already included in set A. Therefore, the remaining numbers that are in S but not in A are 7, 9, and 10.

11. Jika semua anggota himpunan A menjadi anggota himpunan B, maka dikatakan behwa ...

not-available-via-ai

Explanation

not-available-via-ai

12. Diketahui A={1,2,3}, B={2,3,4,5}, C={0,1,2,3,4}, dan D = { }. Diantara pernyataan berikut yang benar adalah ...

D A

A B

B C

C D

The correct answer is D A because it states that D is a subset of A. In set theory, a subset is a set that contains elements that are also found in another set. In this case, since D is an empty set, it does not contain any elements. Therefore, it can be considered a subset of any set, including A.

Explanation

The correct answer is D A because it states that D is a subset of A. In set theory, a subset is a set that contains elements that are also found in another set. In this case, since D is an empty set, it does not contain any elements. Therefore, it can be considered a subset of any set, including A.

13.

Anggota dari A' adalah ...

{1,2,3,4,5}

{1,2,4,5}

{7,8, 10, 11}

{7,8,9,10,11,12}

The correct answer is {7,8,9,10,11,12} because it is the only option that includes all the elements from set A'. The other options either have missing elements or include extra elements that are not part of A'.

Explanation

The correct answer is {7,8,9,10,11,12} because it is the only option that includes all the elements from set A'. The other options either have missing elements or include extra elements that are not part of A'.

14. Jika P = {d,e,f} maka banyaknya himpunan bagian yang mungkin dari P adalah ...

3

6

8

9

The correct answer is 8 because when we have a set with 3 elements (d, e, f), the number of possible subsets can be found by using the formula 2^n, where n is the number of elements in the set. In this case, 2^3 = 8, so there are 8 possible subsets of the set P.

Explanation

The correct answer is 8 because when we have a set with 3 elements (d, e, f), the number of possible subsets can be found by using the formula 2^n, where n is the number of elements in the set. In this case, 2^3 = 8, so there are 8 possible subsets of the set P.