If U = {1, 2, ..., 30}, A is the set of numbers divisible by 2, and B is the set of numbers divisible by 3, what is |A' ∪ B'|?
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Answer and explanation
Correct answer: 25
Use De Morgan’s law: A' ∪ B' = (A ∩ B)'. A ∩ B consists of numbers divisible by both 2 and 3, or equivalently by their least common multiple, 6. Between 1 and 30 these are 6, 12, 18, 24, and 30, so there are 5 such numbers. Therefore |A' ∪ B'| = 30 − 5 = 25, making option C correct.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
Use De Morgan’s law: A' ∪ B' = (A ∩ B)'. A ∩ B consists of numbers divisible by both 2 and 3, or equivalently by their least common multiple, 6. Between 1 and 30 these are 6, 12, 18, 24, and 30, so there are 5 such numbers. Therefore |A' ∪ B'| = 30 − 5 = 25, making option C 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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