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Set Theory Questions

Practice 59 Set Theory questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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57
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Practice by Exam:Mathematics(18)Quantitative Aptitude(18)General Intelligence & Reasoning(7)Mathematics and Science(6)General Intelligence and Reasoning(5)Reasoning Ability(3)Reasoning(2)

About Set Theory — practice questions, PYQs & concepts

Set Theory is a frequently-tested topic on Mathematics, Quantitative Aptitude, General Intelligence & Reasoning. ExamTest.live currently lists 59 Set Theory questions spanning previous-year papers from 2017 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Set Theory weight in competitive exams

Across our Set Theory question bank, the largest sources are Mathematics (18), Quantitative Aptitude (18), General Intelligence & Reasoning (7), Mathematics and Science (6) and General Intelligence and Reasoning (5). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 0 easy Set Theory questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
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All Set Theory Questions(1–59 of 59)

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Q1mediummcqMathematicsMathematics Mock Test - 62026
18% accuracy
Which of the following is an empty set?
Q2mediummcqMathematicsMathematics Mock Test - 102026
8% accuracy
Let be the relation on the set of all real numbers defined by if . Then is:
Q3mediummcqMathematicsMathematics Mock Test - 12026
8% accuracy
Let be the set of all persons living in a city. Persons are said to be related as if is at least years older than . Which one of the following is correct?
Q4mediummcqMathematicsMathematics Mock Test - 12026
0% accuracy
If is a binary operation on defined by the table below:∗12345111111212121311311412141511115Find the value of .
Q5mediummcqGeneral Intelligence & ReasoningCompetitive Exam Practice2026
33% accuracy
Study the diagram given below and answer the question that follows.What number of students have sketch colours, crayons as well as pencil colours?(Assume a Venn diagram with intersecting regions where the central common intersection region of all three shapes equals 5).
image
Q6mediummcqQuantitative AptitudeCompetitive Exam Practice Paper2026
0% accuracy
In a class of students, students play cricket and students play tennis, and students play both the games. Then the number of students who play neither of the two games is :
Q7mediummcqQuantitative AptitudeUP Police Constable2026
50% accuracy
In a survey of , like to play video games, like to play indoor games, and like to play outdoor games. Additionally, like to play both indoor and outdoor games, , , and . Use the Venn diagram to find the students who play only outdoor games.
Q8mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
If , then is:
Q9mediummcqQuantitative AptitudeMock Test2026
0% accuracy
In a survey of people, like tea, like coffee, and like both tea and coffee. How many people like neither tea nor coffee?
Q10mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
A coin is tossed twice. If and denote the occurrence of a head on the first toss and second toss respectively, then what is equal to?
Q11mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If and are two sets such that number of elements in is , number of elements in is and number of elements in both and is , find .
Q12mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
Based on a survey of students, students like cold drinks, students like milkshakes, and students like both. How many students like at least one of the drinks?
Q13mediummcqQuantitative AptitudeCompetitive Exams2026
A regional survey showed that persons read an English newspaper, persons read a Bengali newspaper, and persons read both papers. If persons do not read any newspaper, how many people were surveyed in total?
Q14mediummcqQuantitative AptitudeCompetitive Exam2026
In an examination passed in Maths, passed in Bengali, in both and students failed in both subjects. Then the number of students appeared are:
Q15mediummcqGeneral Intelligence & ReasoningCompetitive Exam2026
In a group of persons travelling in a bus, persons can speak French, can speak Spanish and can speak English. In that group, none can speak any other language. If persons in the group can speak two languages and one person can speak all the three languages, then how many persons are there in the group?
Q16mediummcqGeneral Intelligence and ReasoningCompetitive Exams2026
Rohan ranks seventh from the top and twenty-sixth from the bottom in a class. How many students are there in the class?
Q17mediummcqGeneral Intelligence and ReasoningCompetitive Exams2026
Which of the following sets is best represented by a standard Venn diagram consisting of three concentric circles?
image
Q18mediummcqQuantitative AptitudeCompetitive Examination2026
A survey shows that of the Indians like apples, whereas like oranges. What percentage of Indians like both apples and oranges?
Q19mediummcqGeneral Intelligence & ReasoningCompetitive Exam2026
A Venn diagram shows people who bought ice-cream and drinks in a theatre. Only Ice-cream buyers = , only Drink buyers = . Ice-cream is sold for and drinks for . If a total of is spent, how many people bought both a drink and an ice-cream?

image
Q20mediummcqQuantitative AptitudeCompetitive Exams2026
In a class of students, have chosen only Biology and have chosen Mathematics, but not Biology. Given that every student has chosen either Mathematics, or Biology, or both. Find the number of students who chose both Mathematics and Biology.
Q21mediummcqGeneral Intelligence & ReasoningSSC CGL2026
In the following figure, the rectangle represents Mechanics, the circle represents Artists, the triangle represents Gamers and the square represents Golfers. Which set of letters represents Mechanics who are either Artists or Gamers?

image
Q22mediummcqQuantitative AptitudePractice Test2026
If and are two sets such that the number of elements in is , the number of elements in is and the number of elements in both and is , find .
Q23mediummcqQuantitative AptitudeUP Police Constable2026
Based on a survey of 200 students, 140 students like cold drinks, 120 students like milkshakes, and 80 students like both. How many students like at least one of the drinks?
Q24mediummcqMathematicsAIEEE 20092026
If and are three sets such that and , then:
Q25mediummcqQuantitative AptitudeCompetitive Exam2026
In an examination, of the candidates fail in Bengali and in English. If fail in Bengali and English, the percentage of those passing in both subjects is:
Q26mediummcqQuantitative AptitudeCompetitive Examination2026
In a class of students, passed in mathematics, students passed in statistics and in both subjects. Then the number of students who failed in both subjects is:
Q27mediummcqQuantitative AptitudeCompetitive Exams2026
A survey shows that of Indians like apples, whereas like oranges. What percentage of Indians like both apples and oranges?
Q28mediummcqQuantitative AptitudeCompetitive Exam2026
In an examination, of students fail in Mathematics and fail in English. If fail in both subjects, the total pass percentage is:
Q29mediummcqGeneral Intelligence & ReasoningCompetitive Exam Practice2026
A survey of 1000 persons with respect to their knowledge of Hindi (H), English (E) and Sanskrit (S) yields the following standard data values:

image

What is the ratio of those who know all the three languages to those who do not know Sanskrit?
Q30mediummcqMathematicsCompetitive Exam Practice Paper2026
Direction: Refer to the Venn diagram in the given image image_b95340.png showing the number of Bengali students of age 18 attending certain online courses during complete lockdown:
The square represents the students who are learning Spanish, the triangle is for those who are learning music, and the circle is for those who are learning photography. Study the diagram and answer the question.

image

What approximately is the percentage of students who are learning one thing only?
Q31mediummcqMathematicsCompetitive Exam Practice Paper2026
Direction: Refer to the Venn diagram in the given image image_b9b8db.png showing the number of Bengali students of age 18 attending certain online courses during complete lockdown:

image

The square represents the students who are learning Spanish, the triangle is for those who are learning music, and the circle is for those who are learning photography. Study the diagram and answer the question.

What approximately is the percentage of students who are learning only two things?
Q32mediummcqMathematicsCompetitive Exam Practice Paper2026
Direction: Refer to the Venn diagram in the given image image_b9b8db.png showing the number of Bengali students of age 18 attending certain online courses during complete lockdown:
image

The square represents the students who are learning Spanish, the triangle is for those who are learning music, and the circle is for those who are learning photography. Study the diagram and answer the question.

How many students are enrolled in Spanish?
Q33mediummcqReasoning AbilityCompetitive Exam2026
Refer to the given image_b9bc25.png for Q.123.
Direction: In the Venn diagram given below, the number of Bengali students of age 18 attending certain online courses during complete lockdown is as follows:

image

The square represents the students who are learning Spanish, the triangle is for those who are learning music, and the circle is for those who are learning photography. Study the diagram and answer the question.

The number of students learning photography is how much more/less than the students who are learning Spanish?
Q34mediummcqQuantitative AptitudeCompetitive Exam2026
It has been seen in a survey of a region that persons read English newspaper, persons read Bengali newspaper and persons read both the papers. If persons do not read any paper, on how many people has the survey been done?
Q35mediummcqQuantitative AptitudeWest Bengal Civil Services2026
In an examination students fail in Mathematics, fail in English. If fail in both, the pass percentage is:
Q36mediummcqMathematicsCompetitive Exam Practice Paper2026
A result of a survey of 1000 persons with respect to their knowledge of Hindi (H), English (E) and Sanskrit (S) is given below:

image

What is the ratio of those who know all the three languages to those who do not know Sanskrit?
Q37mediummcqGeneral Intelligence and ReasoningPractice Test2026
Which of the following statements accurately describes the categorical relationship and overlap between 'fruits', 'apples', and 'red objects'?
Q38mediummcqMathematicsAIEEE2026
Let and be a relation on the set . The relation is:
Q39mediummcqMathematicsAIEEE2026
Consider the following relations:;. Then:
Q40mediummcqMathematicsMathematics Mock Test - 32026
Let be a relation on the set of natural numbers defined by . Which one of the following is correct?
Q41mediummcqMathematicsMathematics Mock Test - 32026
The identity element for the binary operation defined on as is:
Q42mediummcqMathematicsMathematics Mock Test - 112026
If and is a relation defined on such that . Then the relation is:
Q43mediummcqGeneral Intelligence & ReasoningCompetitive Exam2026
If in a group of people, like tea, like coffee, and like both tea and coffee, how many people like only tea?
Q44mediummcqMathematicsCompetitive Exam2026
Out of the guests invited to the New Year's party, opted for Indian food, had Italian food, and had Continental food. Additionally, guests had both Indian and Italian food, had both Italian and Continental food, and had both Indian and Continental food. Seven guests had all three types of food. How many guests did not attend the party?
Q45mediummcqReasoningAUT-242026
In a survey, it was discovered that 21 individuals read English newspapers, 26 individuals read Hindi newspapers, and 29 individuals read regional language newspapers. Furthermore, 14 individuals read both English and Hindi newspapers, 15 individuals read both Hindi and regional language newspapers, 12 individuals read both English and regional language newspapers, and 8 individuals read all three types of newspapers. How many people read only regional language newspapers?
Q46mediummcqGeneral Intelligence & ReasoningCompetitive Exam2026
In a survey of people, have visited Delhi, have visited Mumbai and have visited both cities. What is the ratio of the number of people who visited only Delhi to those who visited only Mumbai?
Q47mediummcqReasoning AbilityPractice Test2026
In a diagram:
1. Rectangle shows people who eat Apples
2. Ellipse shows people who eat Bananas
3. Triangle shows people who eat Cherries

image

Which letter(s) in the diagram represent those people who eat only bananas (neither apples nor cherries)?
Q48mediummcqReasoning AbilityPractice Test2026
If and are two sets where the number of elements in set is , the number of elements in set is , and the number of elements common to both sets and is , determine .
Q49mediummcqQuantitative AptitudeCompetitive Exam2026
In a village, of families have a cow, of families have a buffalo and each of the of families has both a cow and a buffalo. In all, there are families in the village. How many families do not have a cow or a buffalo?
Q50mediummcqGeneral Intelligence and ReasoningPractice Test2026
In the given Venn diagram, the Triangle represents people who like Orange juice, the Circle represents people who like Avocado juice, and the Rectangle represents people who like Lime juice. Find the number of people who like only Lime juice.

image
Q51mediummcqGeneral Intelligence and ReasoningPractice Test2026
image
Select the Venn diagram that accurately depicts the relationship between the sets 'Electric vehicles', 'Cars', and 'Bicycles', considering overlap and mutually exclusive categories.
Q52mediummcqMathematicsPractice Paper2026
In a survey, it was discovered that individuals read English newspapers, individuals read Hindi newspapers, and individuals read regional language newspapers. Furthermore, individuals read both English and Hindi newspapers, individuals read both Hindi and regional language newspapers, individuals read both English and regional language newspapers, and individuals read all three types of newspapers. How many people read only regional language newspapers?
Q53mediummcqReasoningUP Police Constable2026
In a class of students, students passed in Mathematics, students passed in Chemistry and students passed in both Mathematics and Chemistry. Then the number of students that failed in both the subjects are:
Q54mediummcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2017
If A={x:x is a letter in word BELOW}, B={x:x is a letter in word WOOL} and C=A−B, then the number of subsets of C is
Q55mediummcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2017
If A and B are non-empty subsets of a set C, then A∪(A∩B) is equal to
Q56hardmcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2017
If A and B are any two sets such that AΔB=A, then A∩B is equal to
Q57mediummcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2017
If , and , then the number of subsets of is
Q58mediummcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2017
If A and B are non-empty subsets of a set C, then A ∪ (A ∩ B) is equal to
Q59hardmcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2017
If A and B be any two sets such that A Δ B = A, then A ∩ B is

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Set Theory questions are commonly asked in Mathematics, Quantitative Aptitude, General Intelligence & Reasoning, Mathematics and Science, General Intelligence and Reasoning. You can filter by exam using the links above.
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Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.