If U = {x : x ∈ N, x ≤ 24}, A is the set of multiples of 2, and B is the set of multiples of 3, what is |(A ∩ B)'|?
Answer and explanation
Correct answer: 20
The intersection A ∩ B consists of numbers that are multiples of both 2 and 3, hence multiples of lcm(2,3) = 6. Within U = {1, 2, ..., 24}, these are 6, 12, 18, and 24, so the intersection has 4 elements. The complement is taken in U, which has 24 elements. Therefore, |(A ∩ B)'| = 24 − 4 = 20, making option C correct.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The intersection A ∩ B consists of numbers that are multiples of both 2 and 3, hence multiples of lcm(2,3) = 6. Within U = {1, 2, ..., 24}, these are 6, 12, 18, and 24, so the intersection has 4 elements. The complement is taken in U, which has 24 elements. Therefore, |(A ∩ B)'| = 24 − 4 = 20, making option C 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).
