If U = {x : x ∈ ℕ, x ≤ 40}, A is the set of numbers divisible by 4, and B is the set of numbers divisible by 6, what is |(A ∩ B)′|?
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Answer and explanation
Correct answer: 37
A number in A ∩ B must be divisible by both 4 and 6. Such numbers are multiples of lcm(4, 6) = 12. In the set {1, 2, …, 40}, these are 12, 24, and 36, so |A ∩ B| = 3. Therefore, the complement contains 40 − 3 = 37 elements. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
37
Why is this the correct answer?
A number in A ∩ B must be divisible by both 4 and 6. Such numbers are multiples of lcm(4, 6) = 12. In the set {1, 2, …, 40}, these are 12, 24, and 36, so |A ∩ B| = 3. Therefore, the complement contains 40 − 3 = 37 elements. Hence, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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