Sets Quiz - ICSE Class 8 Mathematics

Free practice quiz: Sets (ICSE Class 8 Mathematics). 39 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 8 Mathematics practice quiz has 39 multiple-choice questions on Sets, and 39 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. If A = {multiples of 3 between 10 and 25} and B = {even numbers between 15 and 25}, find the number of elements in the intersection of A and B (A ∩ B).

   1. 2
   2. 3
   3. 4
   4. 5
   Show answer

   Answer: A. 2

   Set A consists of multiples of 3 between 10 and 25, so A = {12, 15, 18, 21, 24}. Set B consists of even numbers between 15 and 25, so B = {16, 18, 20, 22, 24}. The intersection A ∩ B contains elements common to both sets. Therefore, A ∩ B = {18, 24}. The number of elements in A ∩ B is 2.

2. If n(X) = 50, n(Y) = 60, and n(X ∪ Y) = 90, find n(X ∩ Y).

   1. 10
   2. 15
   3. 20
   4. 25
   Show answer

   Answer: C. 20

   Using the principle of inclusion-exclusion: n(X ∪ Y) = n(X) + n(Y) - n(X ∩ Y). We are given n(X) = 50, n(Y) = 60, and n(X ∪ Y) = 90. Substituting these values: 90 = 50 + 60 - n(X ∩ Y). 90 = 110 - n(X ∩ Y). Rearranging the equation to solve for n(X ∩ Y): n(X ∩ Y) = 110 - 90 = 20.

3. If A = {x | x is a composite number less than 20} and B = {x | x is a multiple of 3 less than 20}, find the number of elements in A ∩ B.

   1. 3
   2. 4
   3. 5
   4. 6
   Show answer

   Answer: C. 5

   Set A = {composite numbers less than 20} = {4, 6, 8, 9, 10, 12, 14, 15, 16, 18}. So, |A| = 10. Set B = {multiples of 3 less than 20} = {3, 6, 9, 12, 15, 18}. So, |B| = 6. The intersection A ∩ B contains elements that are both composite and multiples of 3, and less than 20. A ∩ B = {6, 9, 12, 15, 18}. The number of elements in A ∩ B is 5.

4. Let A = {x | x is a factor of 36} and B = {x | x is a prime number less than 15}. Find n(A ∪ B).

   1. 10
   2. 11
   3. 12
   4. 13
   Show answer

   Answer: D. 13

   Set A = {factors of 36} = {1, 2, 3, 4, 6, 9, 12, 18, 36}. So, |A| = 9. Set B = {prime numbers less than 15} = {2, 3, 5, 7, 11, 13}. So, |B| = 6. The intersection A ∩ B contains elements that are both factors of 36 and prime numbers less than 15. A ∩ B = {2, 3}. So, |A ∩ B| = 2. Using the principle of inclusion-exclusion: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 9 + 6 - 2 = 15 - 2 = 13.

5. Let A = {x | x is a natural number and x < 5} and B = {x | x is an even natural number and x < 11}. Find the number of elements in A ∪ B.

   1. 5
   2. 6
   3. 7
   4. 8
   Show answer

   Answer: C. 7

   Set A = {natural numbers and x < 5} = {1, 2, 3, 4}. Set B = {even natural numbers and x < 11} = {2, 4, 6, 8, 10}. The union A ∪ B contains all elements that are in A, or in B, or in both. A ∪ B = {1, 2, 3, 4} ∪ {2, 4, 6, 8, 10} = {1, 2, 3, 4, 6, 8, 10}. The number of elements in A ∪ B is 7.

More questions in this quiz

Answers and explanations are in the full quiz.

1. Let U be the set of all integers from 1 to 25. If A = {multiples of 4 in U} and B = {prime numbers in U}, find the number of elements in (A ∪ B)'.
2. Let U = {all integers from 1 to 35}. If P = {multiples of 5 in U} and Q = {multiples of 6 in U}, find the number of elements in P ∪ Q.
3. If n(A) = 20, n(B) = 35, and n(A ∩ B) = 12, find n(A ∪ B).
4. In a class of 50 students, 30 play cricket, 25 play football, and 10 play both. How many students play neither cricket nor football?
5. If A = {x | x is a prime number less than 20} and B = {x | x is an odd number less than 20}, find the number of elements in A ∩ B.
6. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. If A = {factors of 12} and B = {multiples of 3 in U}, find the number of elements in A' ∪ B'.
7. Let A = {vowels in the English alphabet} and B = {letters in the word 'EDUCATION'}. Find the number of elements in A ∩ B.
8. Let A = {multiples of 4 less than 30} and B = {multiples of 6 less than 30}. Find the number of elements in A - B.
9. If A ⊂ B, then which of the following is true?
10. Let U = {positive integers less than 10}. If A = {even numbers in U} and B = {prime numbers in U}, find n(A ∪ B).
11. If A = {x | x is a natural number and 10 ≤ x ≤ 20} and B = {x | x is a prime number and 10 ≤ x ≤ 20}, find the number of elements in A ∩ B.
12. In a survey of 100 students, 60 liked coffee, 50 liked tea, and 30 liked both. How many students liked neither coffee nor tea?
13. Let A = {x | x is a factor of 36} and B = {x | x is a multiple of 4, x ≤ 36}. Find the number of elements in A ∪ B.
14. Let U = {all integers from 1 to 25}. If A = {perfect squares in U} and B = {multiples of 3 in U}, find n(A ∪ B).
15. If n(A) = 30, n(B) = 40, and n(A ∪ B) = 60, find n(A ∩ B).
16. In a class of 40 students, 15 play Tennis, 20 play Badminton, and 10 play Squash. 5 play Tennis and Badminton, 6 play Badminton and Squash, 7 play Tennis and Squash, and 8 play all three games. How many students play none of these games?
17. Let A = {x | x is an integer, 0 < x < 10} and B = {x | x is a prime number, 0 < x < 10}. Find the number of elements in A - B.
18. If A and B are disjoint sets and n(A) = 15, n(B) = 22, find n(A ∪ B).
19. Let A = {x | x is a multiple of 3 and x < 25} and B = {x | x is a multiple of 4 and x < 25}. Find the number of elements in A ∩ B.
20. If A ∩ B = ∅, which of the following is true?
21. Which of the following represents the set of all even numbers from 1 to 10?
22. If A = {apple, banana, cherry} and B = {banana, date, fig}, what is A ∪ B?
23. Let A = {1, 3, 5, 7} and B = {2, 3, 4, 5}. What is A ∩ B?
24. If U = {1, 2, 3, 4, 5, 6} and A = {2, 4, 6}, what is A'?
25. Which of the following is an empty set?
26. Let A = {factors of 18} and B = {multiples of 3 less than 18}. Find the number of elements in A ∩ B.
27. If A = {vowels in the English alphabet} and B = {consonants in the English alphabet}, what is A ∩ B?
28. If A = {1, 2, 3} and B = {3, 4, 5}, find A △ B (symmetric difference).
29. Let U = {all alphabets}. If A = {vowels} and B = {letters in 'RHYTHM'}. Find n(A ∪ B).
30. Let U = {all alphabets}. If A = {vowels} and B = {consonants}. Find n(A ∪ B).
31. Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}. What is the cardinality of A △ B?
32. If A is a set such that A ∪ A = A, then A is called:
33. In a class, 30 students passed in English, 20 passed in Hindi, and 10 passed in both. How many students passed in at least one of the subjects?
34. Let A = {squares of the first five natural numbers} and B = {cubes of the first three natural numbers}. Find the number of elements in A ∪ B.

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