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.
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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).
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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.
If n(X) = 50, n(Y) = 60, and n(X ∪ Y) = 90, find n(X ∩ Y).
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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.
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.
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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.
Let A = {x | x is a factor of 36} and B = {x | x is a prime number less than 15}. Find n(A ∪ B).
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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.
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.
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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.