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About Sets — Class 8 ICSE

Apply set operations to solve problems; use Venn diagrams for two and three sets. This topic is part of the ICSE Class 8 mathematics syllabus (chapter: Chapter 15). On this page you can practice 59 questions across three difficulty levels — 20 easy, 20 medium, and 19 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Sets

  • Introduction to Sets: The Foundation of Grouping
  • Types of Sets and Basic Operations: Union and Intersection
  • More Set Operations: Difference and Complement
  • Advanced Applications: Venn Diagrams for Three Sets
  • Summary, Connections, and Exam Preparation

Interactive lesson · about 15 minutes · checkpoint question after every unit

Sets — solved examples for Class 8 ICSE

Example 1easy

Rohan states that 'the collection of all delicious fruits' is a set. Which of the following statements correctly evaluates Rohan's claim?
  1. A)A. Rohan is correct because fruits are a well-defined category.
  2. B)B. Rohan is incorrect because 'delicious' is subjective and not well-defined.
  3. C)C. Rohan is correct because any collection of objects can be considered a set.
  4. D)D. Rohan is incorrect because a set must contain only numbers.

Step-by-step solution

  1. Step 1: Understand the definition of a set. A set is a well-defined collection of distinct objects. 'Well-defined' means there is no ambiguity about whether an object belongs to the set or not.
  2. Step 2: Analyze Rohan's collection. The term 'delicious' is subjective. What one person considers delicious, another might not. There is no clear criterion to decide if a fruit is 'delicious' for everyone.
  3. Step 3: Conclude based on the definition. Since the criterion 'delicious' is not well-defined, the collection 'all delicious fruits' cannot form a set.

Answer: B. Rohan is incorrect because 'delicious' is subjective and not well-defined.

Example 2medium

Which of the following sets represents the set of prime numbers less than 15?
  1. A)A. {1, 2, 3, 5, 7, 11, 13}
  2. B)B. {2, 3, 5, 7, 11, 13}
  3. C)C. {2, 3, 5, 7, 9, 11, 13}
  4. D)D. {1, 3, 5, 7, 11, 13}

Step-by-step solution

  1. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
  2. List the prime numbers less than 15: These are 2, 3, 5, 7, 11, 13.
  3. Therefore, the set of prime numbers less than 15 is {2, 3, 5, 7, 11, 13}.

Answer: B. {2, 3, 5, 7, 11, 13}

Example 3hard

Which of the following statements is **always true** for any set A?
  1. A)A ∪ ∅ = ∅
  2. B)A ∩ U = ∅ (where U is the universal set)
  3. C)∅ ⊆ A
  4. D)A ⊂ A

Step-by-step solution

  1. Option (A) is incorrect: A ∪ ∅ = A, not ∅. The union of any set with the empty set is the set itself.
  2. Option (B) is incorrect: A ∩ U = A, not ∅. The intersection of any set with the universal set is the set itself.
  3. Option (C) is correct: By definition, the empty set (∅) is a subset of every set, including itself and any given set A. This is a fundamental axiom of set theory.
  4. Option (D) is incorrect: A ⊂ A means A is a proper subset of A. A set cannot be a proper subset of itself, as a proper subset must contain fewer elements than the original set. A ⊆ A (A is a subset of A) would be true, but A ⊂ A is false.

Answer: ∅ ⊆ A

Practice questions on Sets

  1. Q1.easy

    Which of the following represents the set A = {x | x is an integer, -2 ≤ x < 3} in roster form?
    1. A)A. {-2, -1, 0, 1, 2}
    2. B)B. {-2, -1, 0, 1, 2, 3}
    3. C)C. {-1, 0, 1, 2}
    4. D)D. {-3, -2, -1, 0, 1, 2}
    Show answer

    Answer: A. {-2, -1, 0, 1, 2}

    Hint: Remember that integers include positive numbers, negative numbers, and zero. Pay attention to the inequality signs, especially whether they include the endpoints.

  2. Q2.easy

    Which of the following is the correct set-builder form for the set P = {5, 10, 15, 20}?
    1. A)A. P = {x | x is a multiple of 5, x < 25}
    2. B)B. P = {x | x is a natural number, x ≤ 20}
    3. C)C. P = {x | x is an odd number, x ≤ 20}
    4. D)D. P = {x | x is a factor of 20}
    Show answer

    Answer: A. P = {x | x is a multiple of 5, x < 25}

    Hint: Look for a common property shared by all elements in the set and ensure the condition correctly defines the range.

  3. Q3.easy

    Which of the following statements correctly identifies an empty set?
    1. A)A. The set of even prime numbers.
    2. B)B. The set {0}.
    3. C)C. The set of natural numbers less than 1.
    4. D)D. The set of integers whose square is 9 and are even.
    Show answer

    Answer: D. The set of integers whose square is 9 and are even.

    Hint: An empty set contains no elements. Carefully examine each option to see if any element can logically satisfy its condition.

  4. Q4.medium

    Which of the following statements is TRUE?
    1. A)A. The set of all even prime numbers is an empty set.
    2. B)B. The set of natural numbers greater than 100 is a finite set.
    3. C)C. The set {x | x is an integer and x² = 4} is a singleton set.
    4. D)D. The set of all integers less than 0 is an an infinite set.
    Show answer

    Answer: D. The set of all integers less than 0 is an an infinite set.

    Hint: Carefully consider the definition of each type of set (empty, finite, infinite, singleton) and the elements within each described set.

  5. Q5.medium

    In a class of 50 students, 30 students like Math, 25 students like Science, and 10 students like both Math and Science. How many students like at least one of the two subjects?
    1. A)A. 45
    2. B)B. 55
    3. C)C. 65
    4. D)D. 35
    Show answer

    Answer: A. 45

    Hint: Use the formula for the union of two sets: n(M ∪ S) = n(M) + n(S) - n(M ∩ S).

  6. Q6.medium

    Given set A = {2, 4, 6, 8}. Which of the following is NOT a subset of A?
    1. A)A. {2, 6}
    2. B)B. {8}
    3. C)C. {1, 4}
    4. D)D. {}
    Show answer

    Answer: C. {1, 4}

    Hint: A set B is a subset of A if every element of B is also an element of A. The empty set is a subset of every set.

  7. Q7.hard

    Let U = {x | x is an integer, 1 ≤ x ≤ 10}. A = {x | x is a prime number}, B = {x | x is an even number}. Find (A ∪ B)' ∩ A.
    1. A)∅
    2. B){1, 9}
    3. C){2, 3, 5, 7}
    4. D){1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
    Show answer

    Answer: ∅

    Hint: First, list the elements of each set based on their definitions. Then, apply the set operations step-by-step, starting from the innermost parentheses.

  8. Q8.hard

    In a survey of 100 students, 60 passed in Mathematics, 50 passed in Science, and 30 passed in both. How many students failed in both subjects?
    1. A)10
    2. B)20
    3. C)30
    4. D)40
    Show answer

    Answer: 20

    Hint: First, determine the number of students who passed in at least one subject using the principle of inclusion-exclusion. Then, subtract this from the total number of students to find those who failed in both.

  9. Q9.hard

    Consider two sets A and B represented by overlapping circles in a Venn diagram. Which of the following set expressions represents the region that includes elements belonging to A but not B, OR elements belonging to B but not A?
    1. A)A ∩ B
    2. B)(A ∪ B)'
    3. C)(A ∪ B) - (A ∩ B)
    4. D)(A ∩ B)'
    Show answer

    Answer: (A ∪ B) - (A ∩ B)

    Hint: Break down the desired region into simpler parts. The phrase 'elements belonging to A but not B' and 'elements belonging to B but not A' describe specific non-overlapping sections of a Venn diagram.

These are 9 of the 59 questions available for Sets. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.