If U = {1, 2, …, 50}, A = {x : x is divisible by 4}, and B = {x : x is divisible by 6}, what is |A′ ∩ B|?
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Answer and explanation
Correct answer: 4
Within U, the set B consists of the multiples of 6: 6, 12, 18, 24, 30, 36, 42, and 48, so |B| = 8. Numbers belonging to both A and B must be divisible by lcm(4, 6) = 12. These are 12, 24, 36, and 48, so |A ∩ B| = 4. Hence |A′ ∩ B| = |B| − |A ∩ B| = 8 − 4 = 4.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Within U, the set B consists of the multiples of 6: 6, 12, 18, 24, 30, 36, 42, and 48, so |B| = 8. Numbers belonging to both A and B must be divisible by lcm(4, 6) = 12. These are 12, 24, 36, and 48, so |A ∩ B| = 4. Hence |A′ ∩ B| = |B| − |A ∩ B| = 8 − 4 = 4.
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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