Let A = {x ∈ ℕ : 1 ≤ x ≤ 30 and x is a multiple of 2} and B = {x ∈ ℕ : 1 ≤ x ≤ 30 and x is a multiple of 3}. How many elements are in A ∩ B?
Answer and explanation
Correct answer: 5; A ∩ B = {6, 12, 18, 24, 30}
The intersection A ∩ B contains numbers that belong to both sets, so each number must be divisible by both 2 and 3. Such numbers are multiples of lcm(2, 3) = 6. The multiples of 6 from 1 through 30 are 6, 12, 18, 24, and 30. Therefore, A ∩ B has 5 elements, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
5; A ∩ B = {6, 12, 18, 24, 30}
Why is this the correct answer?
The intersection A ∩ B contains numbers that belong to both sets, so each number must be divisible by both 2 and 3. Such numbers are multiples of lcm(2, 3) = 6. The multiples of 6 from 1 through 30 are 6, 12, 18, 24, and 30. Therefore, A ∩ B has 5 elements, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
