If U = {1, 2, …, 90}, A = {x ∈ U : 6 divides x}, and B = {x ∈ U : 10 divides x}, what is n((A ∩ B)')?
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Answer and explanation
Correct answer: 87
An element belongs to A ∩ B only when it is divisible by both 6 and 10. Such numbers are multiples of lcm(6, 10) = 30. In U = {1, 2, …, 90}, the multiples of 30 are 30, 60, and 90, so n(A ∩ B) = 3. Since U has 90 elements, the complement has 90 − 3 = 87 elements. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
87
Why is this the correct answer?
An element belongs to A ∩ B only when it is divisible by both 6 and 10. Such numbers are multiples of lcm(6, 10) = 30. In U = {1, 2, …, 90}, the multiples of 30 are 30, 60, and 90, so n(A ∩ B) = 3. Since U has 90 elements, the complement has 90 − 3 = 87 elements. Therefore, option A 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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