Loading...

About Sets — Class 7 ICSE

Perform operations on sets including union, intersection, complement, and Venn diagram applications. This topic is part of the ICSE Class 7 mathematics syllabus (chapter: Chapter 14). On this page you can practice 53 questions across three difficulty levels — 20 easy, 19 medium, and 14 hard — each with a visual step-by-step solution, plus a timed 31-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 Collections?
  • Types of Sets and Union Operation
  • Intersection and Difference of Sets
  • Universal Set and Complement of a Set
  • Venn Diagrams and Problem Solving

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

Sets — solved examples for Class 7 ICSE

Example 1easy

Which of the following collections IS NOT a well-defined set?
  1. A)A. The collection of all even numbers less than 10.
  2. B)B. The collection of all students in your class taller than 150 cm.
  3. C)C. The collection of all difficult math problems in your textbook.
  4. D)D. The collection of all capital cities of Indian states.

Step-by-step solution

  1. A set must be a well-defined collection of distinct objects, meaning there is an objective criterion for membership.
  2. The term 'difficult' is subjective and varies from person to person. What one student finds difficult, another might find easy.
  3. Therefore, the collection of 'difficult math problems' is not well-defined, as there's no clear, unambiguous way to determine which problems belong to the collection.
  4. Options A, B, and D have clear and objective criteria for membership (even numbers, height, capital cities), making them well-defined sets.

Answer: C. The collection of all difficult math problems in your textbook.

Example 2medium

Which of the following collections is a well-defined set?
  1. A)A) The collection of all intelligent students in your class.
  2. B)B) The collection of beautiful flowers in a garden.
  3. C)C) The collection of even numbers less than 10.
  4. D)D) The collection of famous cricketers in India.

Step-by-step solution

  1. A set is a well-defined collection of distinct objects. This means there should be no ambiguity in deciding whether an object belongs to the set or not.
  2. Options A, B, and D involve subjective terms like 'intelligent', 'beautiful', and 'famous', which vary from person to person. Therefore, they are not well-defined.
  3. Option C, 'The collection of even numbers less than 10', clearly defines its elements as {2, 4, 6, 8}. There is no ambiguity.

Answer: C) The collection of even numbers less than 10.

Example 3hard

Which of the following statements is ALWAYS true for any non-empty set A within a universal set U?
  1. A)A - ∅ = ∅
  2. B)A ∪ U = ∅
  3. C)∅ ∩ A = ∅
  4. D)U - A = A

Step-by-step solution

  1. A - ∅ = A, as removing no elements from A leaves A itself. So, option (A) is false.
  2. A ∪ U = U, as the union of any set with the universal set is the universal set. So, option (B) is false.
  3. ∅ ∩ A = ∅, as the intersection of any set with the empty set will always be empty because there are no common elements. So, option (C) is true.
  4. U - A = A' (the complement of A), not A itself, unless A is empty which contradicts the 'non-empty' condition. So, option (D) is false.

Answer: ∅ ∩ A = ∅

Practice questions on Sets

  1. Q1.easy

    Convert the set A = {x | x is a natural number, 5 < x ≤ 9} into roster form.
    1. A)A. {5, 6, 7, 8, 9}
    2. B)B. {6, 7, 8, 9}
    3. C)C. {6, 7, 8}
    4. D)D. {5, 6, 7, 8}
    Show answer

    Answer: B. {6, 7, 8, 9}

    Hint: Pay close attention to the inequality signs: '<' means 'not including', and '≤' means 'including'. Natural numbers start from 1.

  2. Q2.easy

    Rohan states: 'The set of even prime numbers greater than 2 is a singleton set.' Is Rohan's statement correct? Why or why not?
    1. A)A. Yes, because 4 is an even prime number greater than 2.
    2. B)B. No, because there are no even prime numbers greater than 2, making it an empty set.
    3. C)C. Yes, because 2 is the only even prime number, and Rohan misunderstood the 'greater than 2' part.
    4. D)D. No, because all even numbers are not prime, so there are many such numbers.
    Show answer

    Answer: B. No, because there are no even prime numbers greater than 2, making it an empty set.

    Hint: Recall the definition of a prime number and identify the only even prime number.

  3. Q3.easy

    Which of the following statements correctly distinguishes between a finite set and an infinite set?
    1. A)A. A finite set has some elements, while an infinite set has no elements.
    2. B)B. A finite set has a countable number of elements, while an infinite set has an uncountable number of elements.
    3. C)C. A finite set has elements that are small numbers, while an infinite set has elements that are large numbers.
    4. D)D. A finite set is a subset of an infinite set, but an infinite set cannot be a subset of a finite set.
    Show answer

    Answer: B. A finite set has a countable number of elements, while an infinite set has an uncountable number of elements.

    Hint: Think about whether you can list or count all the elements in the set and eventually finish the counting.

  4. Q4.medium

    If set A = {x | x is a natural number and 3 ≤ x < 8}, then write set A in roster form.
    1. A)A) {3, 4, 5, 6, 7, 8}
    2. B)B) {3, 4, 5, 6, 7}
    3. C)C) {4, 5, 6, 7}
    4. D)D) {4, 5, 6, 7, 8}
    Show answer

    Answer: B) {3, 4, 5, 6, 7}

    Hint: Remember to include natural numbers that are greater than or equal to 3, but strictly less than 8.

  5. Q5.medium

    Which of the following is an example of an empty set?
    1. A)A) {x | x is an even prime number greater than 2}
    2. B)B) {x | x is a natural number less than 5}
    3. C)C) {x | x is a prime number and 10 < x < 15}
    4. D)D) {x | x is a whole number and x ≤ 0}
    Show answer

    Answer: A) {x | x is an even prime number greater than 2}

    Hint: An empty set contains no elements. Think about the unique properties of prime numbers and even numbers.

  6. Q6.medium

    If U = {x | x is a natural number and x ≤ 10}, and A = {x | x is an odd number and x ∈ U}, what is the cardinal number of set A?
    1. A)A) 4
    2. B)B) 6
    3. C)C) 3
    4. D)D) 5
    Show answer

    Answer: D) 5

    Hint: First, list all elements of set U, then identify the odd numbers among them to form set A. Finally, count the elements in A.

  7. Q7.hard

    Let P, Q, R be three non-empty sets. If P ⊆ Q and Q ⊆ R, which of the following must be true?
    1. A)R ⊆ P
    2. B)Q is a proper subset of P
    3. C)P ∪ Q = R
    4. D)P ∩ R = P
    Show answer

    Answer: P ∩ R = P

    Hint: Recall the definition of a subset and think about the transitive property of subsets. If P is a subset of Q, and Q is a subset of R, what does that imply about the elements of P in relation to R?

  8. Q8.hard

    In a class of 50 students, 35 students like Mathematics, and 28 students like Science. Each student likes at least one subject. How many students like ONLY Mathematics?
    1. A)7
    2. B)15
    3. C)22
    4. D)23
    Show answer

    Answer: 22

    Hint: Use the Principle of Inclusion-Exclusion to find the number of students who like both subjects first. Then, subtract this from the total number of students who like Mathematics.

  9. Q9.hard

    In a group of 40 students, it is observed that 25 students like playing Football, and 20 students like playing Cricket. If 12 students like playing ONLY Football, how many students like playing ONLY Cricket?
    1. A)5
    2. B)7
    3. C)8
    4. D)10
    Show answer

    Answer: 7

    Hint: First, use the information about students who like 'only Football' and total Football players to find how many like both sports. Then, use this to find those who like 'only Cricket'.

These are 9 of the 53 questions available for Sets. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.