If U = {1, 2, …, 84}, A = {x : x is divisible by 6}, and B = {x : x is divisible by 14}, what is |(A ∩ B)′|?
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Answer and explanation
Correct answer: 82
A number belongs to both A and B precisely when it is divisible by the least common multiple of 6 and 14. Since lcm(6, 14) = 42, the common elements in U are 42 and 84 only. Thus |A ∩ B| = 2, and the complement contains the remaining 84 − 2 = 82 elements. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
82
Why is this the correct answer?
A number belongs to both A and B precisely when it is divisible by the least common multiple of 6 and 14. Since lcm(6, 14) = 42, the common elements in U are 42 and 84 only. Thus |A ∩ B| = 2, and the complement contains the remaining 84 − 2 = 82 elements. Therefore, option C 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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