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About Sets — Class 6 ICSE

Represent sets using roster and set-builder notation; identify types of sets and perform basic operations. This topic is part of the ICSE Class 6 mathematics syllabus (chapter: Chapter 12). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 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 - What are they?
  • Representing Sets - Roster and Set-Builder Forms
  • Types of Sets
  • Basic Set Operations - Union and Intersection
  • Summary, Connections, and Preparation for Practice

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

Sets — solved examples for Class 6 ICSE

Example 1easy

Which of the following is a well-defined collection and can be called a set?
  1. A)A collection of all tall students in a class
  2. B)A collection of all vowels in the English alphabet
  3. C)A collection of good books
  4. D)A collection of beautiful flowers

Step-by-step solution

  1. A set is a well-defined collection of objects.
  2. The vowels in the English alphabet are clearly defined: a, e, i, o, u. There is no ambiguity.
  3. Terms like 'tall', 'good', and 'beautiful' are subjective and not well-defined.

Answer: A collection of all vowels in the English alphabet

Example 2medium

Express the set A = {x : x is a prime number less than 20} in roster form.
  1. A){2, 3, 5, 7, 11, 13, 17, 19}
  2. B){1, 2, 3, 5, 7, 11, 13, 17, 19}
  3. C){2, 3, 5, 7, 11, 13, 17}
  4. D){2, 4, 6, 8, 10, 12, 14, 16, 18}

Step-by-step solution

  1. Prime numbers less than 20 are those with exactly two factors.
  2. Checking: 2, 3, 5, 7, 11, 13, 17, 19 are all prime.
  3. 1 is not prime (only one factor). So A = {2, 3, 5, 7, 11, 13, 17, 19}.

Answer: {2, 3, 5, 7, 11, 13, 17, 19}

Example 3hard

How many subsets does the set {a, b, c, d} have?
  1. A)8
  2. B)12
  3. C)16
  4. D)4

Step-by-step solution

  1. The set has 4 elements.
  2. Number of subsets = 2^4 = 16.
    24=162^4 = 16
  3. This includes ∅, four 1-element subsets, six 2-element subsets, four 3-element subsets, and the set itself.

Answer: 16

Practice questions on Sets

  1. Q1.easy

    Which symbol is used to denote 'is an element of' a set?
    1. A)∈
    2. B)⊂
    3. C)∪
    4. D)∩
    Show answer

    Answer: ∈

    Hint: This symbol looks like a small curved E and is read as 'belongs to'.

  2. Q2.easy

    If A = {2, 4, 6, 8, 10}, which of the following is true?
    1. A)3 ∈ A
    2. B)5 ∈ A
    3. C)6 ∈ A
    4. D)7 ∈ A
    Show answer

    Answer: 6 ∈ A

    Hint: Check which number from the options is actually listed in set A.

  3. Q3.easy

    Write the set of all natural numbers less than 6 in roster form.
    1. A){1, 2, 3, 4, 5}
    2. B){0, 1, 2, 3, 4, 5}
    3. C){1, 2, 3, 4, 5, 6}
    4. D){1, 2, 3, 4}
    Show answer

    Answer: {1, 2, 3, 4, 5}

    Hint: Natural numbers start from 1. 'Less than 6' means we stop before 6.

  4. Q4.medium

    Which of the following sets is equal to {1, 2, 3}?
    1. A){3, 1, 2}
    2. B){1, 2}
    3. C){1, 2, 3, 4}
    4. D){0, 1, 2, 3}
    Show answer

    Answer: {3, 1, 2}

    Hint: Order does not matter in a set. Two sets are equal if they have exactly the same elements.

  5. Q5.medium

    If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 4, 6, 8, 10}, what is the cardinal number of the set of elements in U but not in A?
    1. A)4
    2. B)5
    3. C)6
    4. D)10
    Show answer

    Answer: 5

    Hint: Find all elements in U that are not in A, then count them.

  6. Q6.medium

    Write the set B = {x : x is a multiple of 3, 3 <= x <= 18} in roster form.
    1. A){3, 6, 9, 12, 15, 18}
    2. B){3, 6, 9, 12, 15}
    3. C){6, 9, 12, 15, 18}
    4. D){1, 3, 6, 9, 12, 15, 18}
    Show answer

    Answer: {3, 6, 9, 12, 15, 18}

    Hint: List all multiples of 3 starting from 3 up to and including 18.

  7. Q7.hard

    If A = {x : x is a factor of 24} and B = {x : x is a factor of 36}, find n(A ∩ B).
    1. A)4
    2. B)6
    3. C)8
    4. D)5
    Show answer

    Answer: 6

    Hint: First list all factors of 24 and 36 separately, then find the common ones.

  8. Q8.hard

    In a class of 40 students, 25 like maths, 22 like science, and 12 like both. How many students like neither subject?
    1. A)3
    2. B)5
    3. C)7
    4. D)10
    Show answer

    Answer: 5

    Hint: First find how many like at least one subject using n(A ∪ B) = n(A) + n(B) - n(A ∩ B). Then subtract from total.

  9. Q9.hard

    If A has 5 elements and B has 3 elements, what is the maximum possible value of n(A ∩ B)?
    1. A)5
    2. B)3
    3. C)8
    4. D)2
    Show answer

    Answer: 3

    Hint: The intersection cannot have more elements than the smaller set.

These are 9 of the 60 questions available for Sets. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.