Worksheet for Class 7 Maths Chapter 8 Sets

A Set is a well-defined collection of objects, numbers, or things that have something in common. In this blog, we have compiled a revision worksheet for Class 7 Maths Chapter 8 Sets with detailed solutions.

The Infinity Learn Class 7 Maths Worksheet on Sets is designed according to the latest CBSE syllabus (2025–26). It includes all important types of questions that usually appear in exams from basic definitions and notations to Venn diagrams and practical examples.

This worksheet will help students to clear their concept of elements, subsets, universal sets, and empty sets, ensuring that students can solve any question with confidence. It also provides step-by-step explanations to understand the logic behind each answer.

Why use Class 7 Maths Sets Worksheet?

It Covers all key topics from the Sets chapter

• Based on the latest CBSE guidelines
• Includes mixed question types (MCQs, fill-ups, and word problems)
• Improves logical thinking and exam readiness

Worksheet for Class 7 Maths Chapter 8 Sets PDF

Class 7 maths Chapter 8 worksheet that can be downloaded as a PDF from Infinity Learn website according to the latest CBSE syllabus. The Sets PDF can be downloaded free of charge and involves higher-level, abstract, and applied questions to enable students to get familiar with concepts of union, intersection, subsets, and Venn diagrams in a simple and systematic manner.

This PDF worksheet can be downloaded and practiced any time by students in order to make sure they reinforce their knowledge of Sets in Class 7 Maths. All questions in the worksheet are aimed at developing logical thinking and increasing the ability to solve problems.

Worksheet for Class 7 Maths Chapter 8 Sets (Advanced Level)

Section A – Basic Concept Questions

Q1. Define a set in your own words. Give two examples from daily life.

Q2. Write all subsets of the set A = {x | x < 5, x ∈ N}.

Q3. State whether the following are sets or not. Give reasons.
a) The collection of beautiful rivers in India.
b) The collection of prime numbers less than 20.
c) The collection of all months starting with “M”.

Q4. If A = {1, 2, 3, 4, 5}, how many subsets does A have?

Q5. Write the set of all letters used in the word “MATHEMATICS” using set-builder form.

Section B – Representation of Sets

Q6. Represent the following using the Roster form:
a) Set of odd numbers less than 15.
b) Set of factors of 18.

Q7. Express the following in Set-builder form:
a) {2, 4, 6, 8, 10}
b) {1, 4, 9, 16, 25}

Q8. If A = {3, 6, 9, 12}, write one universal set U for which A ⊂ U.

Section C – Types of Sets

Q9. Identify the type of each set:
a) A = {x | x is an even number less than 10}
b) B = {}
c) C = {y | y² = 16, y ∈ N}

Q10. If P = {5, 10, 15, 20} and Q = {10, 20, 30, 40}, find:
a) P ∩ Q
b) P ∪ Q
c) P – Q

Q11. Give an example of two disjoint sets and one overlapping set.

Section D – Venn Diagram Questions

Q12. In a school of 100 students,

60 play cricket

45 play football

20 play both games

Find:

a) How many play only cricket?
b) How many play only football?
c) Represent using a Venn diagram.

Q13. Draw a Venn diagram to represent:

A ⊂ B

A ∩ B = Ø

A ∪ B = U

Section E – Real-life Application Questions

Q14. Let A = {students who like Maths}, B = {students who like Science}.

If 20 students like both, 30 like only Maths, and 25 like only Science,
find the total number of students who like at least one subject.

Q15. In a survey, 100 people were asked:

55 like tea

40 like coffee

15 like both tea and coffee

Find the number of people who like only tea, only coffee, and neither.

Section F – Challenge Zone (Advanced Thinking)

Q16. If A = {x | x is a factor of 24} and B = {x | x is a multiple of 3 and x ≤ 24}, find A ∩ B.

Q17. Let U = {1, 2, 3, ..., 20}, A = {multiples of 2}, and B = {multiples of 3}.
Find:
a) A ∩ B
b) A ∪ B
c) (A ∪ B)’

Q18. If n(U) = 50, n(A) = 30, n(B) = 25, and n(A ∩ B) = 10, find:
a) n(A ∪ B)
b) n(A’ ∩ B)

Q19. Let P = {prime numbers less than 15} and Q = {even numbers less than 15}.
Find P ∩ Q and P ∪ Q.

Q20. Write two sets A and B such that:

A ∩ B = {5}

A ∪ B = {1, 3, 5, 7, 9}

Section G – Reasoning & Proof-based

Q21. Prove that if A ⊂ B, then A ∩ B = A.

Q22. Prove that (A ∪ B)’ = A’ ∩ B’ using a Venn diagram.

Q23. If n(A) = 10, n(B) = 8, and n(A ∩ B) = 5, find n(A ∪ B) and n(A’ ∩ B’).

Q24. Justify whether A – (B ∪ C) = (A – B) ∩ (A – C) for sets

 A = {1, 2, 3, 4}, B = {2, 4}, C = {3}.

Q25. A = {a, b, c}, B = {b, c, d, e}. Find (A ∪ B) – (A ∩ B).

Section H – Word Problems (Logical Set Reasoning)

Q26. In a class of 60 students:

25 play Chess

30 play Badminton

10 play both

5 play neither
Find the total number of students who play at least one game.

Q27. If 100 students took part in a survey where 70 like Maths, 60 like English, and 45 like both, how many like only one subject?

Q28. A group of students was asked about owning a pet:

40 have a dog

30 have a cat

15 have both
Find how many students have only one pet.

Q29. In a school, 120 students study Hindi or English. If 80 study Hindi and 70 study English, and 30 study both, how many study only English?

Q30. There are 50 students in a class:

35 like Pizza

25 like Burger

15 like both
Find:
a) Number of students who like only Pizza.
b) Number who like neither Pizza nor Burger.

Section I – Higher Order Thinking (HOTs)

Q31. If A = {x | x² < 30, x ∈ N} and B = {x | x is even, x ≤ 10}, find A ∩ B and A – B.

Q32. The universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9}.

A = {2, 4, 6, 8}, B = {3, 6, 9}, C = {4, 8, 9}.
Find (A ∩ B)’ ∩ C.

Q33. Write two real-life examples where sets help in data classification.

Q34. A and B are such that A ∪ B = A. What can you say about A and B?

Q35. If A and B are disjoint sets, what is A ∩ B? Explain with an example.

Answer Key

Q1. A collection of well-defined objects. Examples: {apple, banana, mango}; {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

Q2. A = {1,2,3,4}. Subsets: ∅, {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}, {1,2,3}, {1,2,4}, {1,3,4}, {2,3,4}, {1,2,3,4}

Q3. a) Not a well-defined set. b) Yes: {2,3,5,7,11,13,17,19}. c) Yes: {March, May}

Q4. 32

Q5. {M, A, T, H, E, I, C, S} (or {x | x is a letter in “MATHEMATICS”})

Q6. a) {1,3,5,7,9,11,13} b) {1,2,3,6,9,18}

Q7. a) {x | x = 2n, n ∈ N, 1 ≤ n ≤ 5} b) {x | x = n², n ∈ N, 1 ≤ n ≤ 5}

Q8. Example U = {1,2,3,...,12}

Q9. a) Finite set {2,4,6,8} b) Empty set Ø c) {4}

Q10. a) {10,20} b) {5,10,15,20,30,40} c) {5,15}

Q11. Disjoint: {1,2} and {3,4}. Overlapping: {1,2,3} and {2,3,4}.

Q12. a) 40 b) 25 c) 15

Q13. (no text — diagrams)

Q14. 75

Q15. Only tea = 40; Only coffee = 25; Neither = 20

Q16. {3,6,12,24}

Q17. a) {6,12,18} b) {2,3,4,6,8,9,10,12,14,15,16,18,20} c) {1,5,7,11,13,17,19}

Q18. a) 45 b) 15

Q19. ∩ Q = {2} P ∪ Q = {2,3,4,5,6,7,8,10,11,12,13,14}

Q20. One choice: A = {1,5,7}, B = {3,5,9}

Q21. A ∩ B = A

Q22. (A ∪ B)’ = A’ ∩ B’

Q23. n(A ∪ B) = 13; n(A’ ∩ B’) = n(U) − 13 (cannot compute without n(U))

Q24. Both sides = {1} (identity holds for given sets)

Q25. (A ∪ B) − (A ∩ B) = {a,d,e}

Q26. Inconsistent as given; if class = 60 and both = 10, then neither = 15 (or change numbers).

Q27. Only one subject = 40

Q28. Only one pet = 40

Q29. Only English = 40

Q30. a) Only Pizza = 20 b) Neither = 5

Q31. A = {1,2,3,4,5}; B = {2,4,6,8,10}; A ∩ B = {2,4}; A − B = {1,3,5}

Q32. (A ∩ B)’ ∩ C = {4,8,9}

Q33. Library: books by subject; Grocery: perishable vs non-perishable items.

Q34. B ⊂ A

Q35. A ∩ B = Ø (example A = {1,2}, B = {3,4})