Let U={1,2,...,60}, A be the set of multiples of 3, and B be the set of multiples of 4. What is n((A∪B)′)?
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Answer and explanation
Correct answer: 30
Among the integers from 1 to 60, there are floor(60/3)=20 multiples of 3 and floor(60/4)=15 multiples of 4. Multiples of both 3 and 4 are multiples of 12, so there are floor(60/12)=5 common elements. Therefore n(A∪B)=20+15−5=30. The complement contains the remaining 60−30=30 elements, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
Among the integers from 1 to 60, there are floor(60/3)=20 multiples of 3 and floor(60/4)=15 multiples of 4. Multiples of both 3 and 4 are multiples of 12, so there are floor(60/12)=5 common elements. Therefore n(A∪B)=20+15−5=30. The complement contains the remaining 60−30=30 elements, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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