Let A = {x ∈ N : x ≤ 12}, B be the set of even natural numbers not exceeding 12, and C be the set of multiples of 3 not exceeding 12. What is n(B ∩ C)?
Answer and explanation
Correct answer: 2
The governing concept is set intersection: B ∩ C contains only numbers satisfying both conditions. The even natural numbers up to 12 are 2, 4, 6, 8, 10, and 12, while the multiples of 3 are 3, 6, 9, and 12. Their common elements are therefore B ∩ C = {6, 12}. Since this set has two elements, n(B ∩ C) = 2, so option A is correct. Options B, C, and D do not match the actual intersection.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The governing concept is set intersection: B ∩ C contains only numbers satisfying both conditions. The even natural numbers up to 12 are 2, 4, 6, 8, 10, and 12, while the multiples of 3 are 3, 6, 9, and 12. Their common elements are therefore B ∩ C = {6, 12}. Since this set has two elements, n(B ∩ C) = 2, so option A is correct. Options B, C, and D do not match the actual intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
