Set Theory Questions and Answers

Set Theory Questions

Formula

Definition of Set Theory

A Set is commonly defined as an assembly of items, recognized as foundations. These items could be any possible thing, including digits, alphabets, colors etc. However, none of the items of the set can be a set in itself.

Presentation of sets:

We mark sets using brackets and signify them with capital letters. The most standard technique to define sets is by enlisting all its items. For example: P= {5, 6, 7, 8, 9, 10…….18} is the set of counting numbers beginning from 5. Q= {Black, white, Red, Yellow…} is a set of colors. R= {-3, -2, -1, ., 1, 2, 3….} is a set of all integers.

Formula or Rule for Set Theory

The set that consists of all the elements of a specified group is called the universal set and is denoted by the symbol ‘µ,’ also known as ‘mu.’ For two sets P and Q, n(PᴜQ) is the number of items existent in either of the sets P or Q. n(P∩Q) is the number of items existent in both the sets P and Q. n(PᴜQ) = n(P) + (n(Q) – n(P∩Q) For three sets P, Q and R, n(PᴜQᴜR) = n(P) + n(B) + n(R) – n(P∩Q) – n(Q∩R) – n(R∩P) + n(P∩Q∩R)

Question 1

Time: 00:00:00
A class had a strength of 40 students numbered from 1 to 40. Students with even roll numbers were doing English literature, while students with roll numbers in multiples of 4 were doing Fashion Design, and students with roll numbers in multiples of 8 were in the technical field.

Calculate the number of students who opted for none of the three streams?

20

20

25

25

30

30

35

35

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Question 2

Time: 00:00:00
A group of tourists were traveling together on a train. 12 Tourists were able to speak Spanish, 30 could speak only French, and 12 could speak German. And no one from that group could speak any other language. If 4 persons in the group were able to speak two languages and 2 people were able to speak all the three languages, then calculate the total number of tourists in that group?

20

20

42

42

35

35

10

10

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Question 3

Time: 00:00:00
A school had 240 students, from which 10% were able to play all the 3 games Basket Ball, Table Tennis and Hockey. 60 students were able to play any and only 2 games. Only 80 Students were able to play Basketball. Calculate the total number of students who were able to play only Table Tennis and only Hockey?

76

76

100

100

150

150

60

60

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Question 4

Time: 00:00:00
In a hostel, 20 residents want to watch football games, and 28 residents want to watch Cricket. However, 10 Residents were ready to watch both Football and Cricket. Calculate the number of residents who wanted to watch only football or Cricket?

10

10

18

18

15

15

20

20

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Question 5

Time: 00:00:00
A class had 120 students, out of which 54 students liked to have Pizza, and 84 preferred to have a Salad. However, each student preferred to have at least one of the two dishes. Calculate the number of students who liked both Pizza and Salad?

50

50

20

20

18

18

70

70

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Question 6

Time: 00:00:00
 In the below-mentioned diagram Triangle represents Girls Square represents Singers, and Circle represents Musicians. Identify the Girls who are both Singers and Musicians?

Eva

Eva

Diya

Diya

Cia

Cia

Bina

Bina

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Question 7

Time: 00:00:00
In a class of 40 students, 12 students selected Spanish and Chinese, 22 students opted for Spanish. However, each student selected at least one of the two languages. Calculate the total number of students who chose only Spanish as their primary learning language and not Chinese?

10

10

20

20

18

18

None of the above

None of the above

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Question 8

Time: 00:00:00
If 70% of the audience prefers to read comic Novels, 90% loves to read Romantic Novels, and 98% like to read Fiction Novels. Calculate the proportion of readers who like to read all three languages?

60%

60%

58%

58%

90%

90%

50%

50%

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Question 9

Time: 00:00:00
In a recent survey conducted in a school, it was discovered that 80 students preferred an I-phone, whereas 60 students went for an Android phone. However, 20 Students were not that particular and accordingly could go with any of them. If each student preferred to have at least one of the items, find out how many students the survey was conducted?

120

120

60

60

100

100

50

50

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Question 10

Time: 00:00:00
An office consisted of 200 Employees, 144 people came by Car, and 86 employees came by bus. Calculate the number of employees who came exclusively via car? How many employees came by Bus only and how many employees traveled both by car and by bus?

114, 56

114, 56

100. 120

100. 120

114, 24

114, 24

104, 35

104, 35

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Question 11

Time: 00:00:00
An office had 400 employees, from which 140 Students played TT, 120 Employees preferred to play Badminton, and 160 employees liked playing Cricket. Moreover 60 employees liked playing both TT and Cricket whereas 60 students preferred to play Badminton and Cricket, and 80 students played both TT and Badminton. If 260 employees preferred to play at least one of the game then how many employees played all the 3 games?

40

40

32

32

44

44

46

46

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Question 12

Time: 00:00:00
A class had 50 students. 35 students liked Chocolates and 30 students liked Cupcakes, and 20 students like both chocolates and Cupcakes. How many students liked Neither Chocolates nor Cupcakes?

 

20

20

15

15

10

10

5

5

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Question 13

Time: 00:00:00
A review was conducted in an office to find the IPhone and android users, hence 200 employees were selected randomly. 140 employees liked I phone, 120 preferred to have android phone instead, while 80 liked both I phones and android phone. Calculate Number of employees who preferred to have at least one of the instrument?

180

180

40

40

60

60

100

100

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Question 14

Time: 00:00:00
A class had a total of 53 students, where each student selected at least one of the three languages English, French, and Spanish. 24 students learned English, 25 opted for French, and 26 Spanish. Moreover 8 scholars who chose to learn both English and French, 9 Students who studied English and Spanish, and 9 students who opted for French and Spanish. Calculate the number of scholars who studied more than 1 language?

25

25

20

20

19

19

15

15

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Question 15

Time: 00:00:00
In the below-mentioned diagram Triangle represents Men Square represents Engineers, and Circle represents Lawyers. Identify the men who are both engineers and lawyers?

E

E

D

D

C

C

B

B

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["0","40","60","80","100"]
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